Richard Whately and the Revival of Syllogistic Logic in Great Britain in the Early Nineteenth Century
It might be interesting to create a Christopher Alexander style Hasse diagram with a partial ordering along with a force of affinity/conflict between each of the character here.
One of the central aspects of the whole thesis seems to be that the epistemological and ontological perspective of the people cast very different light on how they saw logic. As a result of their metaphysical(?) views, the logic became a framework that can be instrumented in different ways. Some of them clubbed induction and deduction under it, some elevated one instead of another.
For example: Stewart at times has + and - with Locke. There is a temporal aspect as well, he was first aligned with Lingua Characteristica in the beginning, but then moved away from it.
Aristotle
Francis Bacon Rene Descartes John Locke (+ Descartes) Arnauld / Pierre Nicole
Aldrich (+ Locke, adopts the terminology of agreement/disagreement of ideas) Isaac Watts (+ Locke, + Port Royal) William Duncan (+ Locke, + Port Royal)
Thomas Reid {Founder of Common Sense Philosophy} (- Hume, - Aldrich’s axiomatic approach, - Locke, - Cartesian Logic) (+ Induction, + Language and thought as closely related, + Bacon, + Induction, + Philosophy of Mind) Lord Kames George Campbell
John William Playfair (1748 – 1819) Dugald Stewart (+ French philosophy, + Reid, Heir of Reid, + Meagre nominalism, + Philosophy of mind, + Condillac (early period), + Leibniz (early period), + Locke (On utility of syllogistic reasoning), + Campbell (On utility of syllogistic reasoning), - Monboddo, - Gillies) Edward Tatham (- Locke on the certainty achievable in mathematics, - Reid on syllogistic reasoning in mathematics) James Beattie Robert Eden Scott (+ Reid, + Stewart, - Stewart (Nominalist outlook)) William Barron (+ Locke, + Arnauld, + Reid) Lord Monboddo (+ Platonic view, + Aristotle, - Reid) John Gillies (+ Aristotle, + Nominalism, - Reid, - Aldrich (Axiomatic Approach)) Francis Balfour (+ Gillies, + Aristotle) George Jardine Richard Murray John Walker (- Locke, + Murray) Richard Kirwan (- Locke, - Campbell, + Syllogism) T K Abbott John Eveleigh (1747 – 1814) John Davison Henry Kett Edward Copleston (+ Gillies, - Playfair, - Reid, + Stewart’s inductive science of mind) Henry Drummond (Grandson of Lord Kames, - Copleston) William Rowe Lyall (- Stewart, - Logic as art) John Hill (1787 – 1855) Richard Whately (1787 – 1863) (+ Copleston, + Kirwan, + Coleridge, ++ Kant, + Logic as art, + Logic as science, + Lyall, + Gillies, + Aldrich, - Tatham (Kinds of evidences for reasoning), - Stewart (Kind sod evidences for reasoning)) John Henry Newman (1801 – 1890) William Monsell William Hamilton (+ Kant) S T Coleridge (+ Kant) George Bentham (- Whately) John Stuart Mill (+ Whately, + Deduction (but changed later to induction))
Doing a transitive closure on Whately gives Kant as he is related to Kant’s view via Coleridge’s writing.
Background: Petrus Ramus Blaise Pascal Isaac Newton Leibniz Condillac David Hume Joseph Marie de Gerdano Jean D’Alembert Herschel George Turnbull (Teacher of Thomas Reid) (+ Induction) John Wallis J G Heineccius Robert Woodhouse Adam Smith Sanderson (whose text was used in Oxford) William Whewell LaPlace John Wallis John Wesley (Co-founder of Methodists) Berkeley Narcissus Marsh Philip Du Trieu Thomas Kingsmill Abbott Franco Burgersdicius H M Mansel Maclaurin Immanuel Kant Jeremy Bentham J Blanco White H M Mansel John Veitch Thomas Spencer Baynes Augustus De Morgan Samuel Neil Alexander Campbell Fraser (Tutor of John Veitch) George Cornewall Lewis (1806 – 1863) Samuel Hinds (1793 – 1872) John Huyshe (1802 – 1880)
Even less James Clow Charles Butler Robert Simson Edmund Burke Charles Wesley (Great nephew of John Wesley) Benjamin Vale (1787/8 – 1863) Francis Hutcheson John Napleton (Book referred in Kett’s text) Robert Buchanan Robert Dodsley (Book on which Duncan’s logic was appended anonymously) John Keble (Founder of Tractarianism / High church movement known as the “Oxford Movement”) Edward Hawkins (1789 – 1882) Renn Dickson Hampden (1793 – 1868) Thomas Arnold (1800 – 1882) William Thomson John Parsons John Wilson / Christopher North (Pen name) Renn Dickson Hampden Edward Tagart Samuel Hinds John Huyshe George Moberly David Ritchie (Predecessor of William Hamilton)
Concepts of Discourse
Nominalism, Gillies interpretation Realism The Problem of Universals Formalism Conceptualism - Port Royal Usage of axioms Euclidean axiomatic science vs. canonical approach Epistemic structures Induction vs. Deduction Scottish Enlightenment (Reid, who else?) Analysis vs. Synthesis Verbal vs. Mental distinction (as seen in Duncan’s logic) Role of Language - Locke, Gillies, Stewart (First position: Language advances human science) Psychologism Sensationalism of Condillac Logic’s scope within mind, purely formal (In)utility of syllogisms/logic (Bacon, Locke, Arnauld, Descartes, Campbell, Stewart, Reid, Kames) Method of analysis as used by Bacon and Newton seems to make it closer to inductive method. It was also used by Campbell. Things vs. Words distinction Induction as a method of reasoning vs. induction as a method of investigation Demonstrating the Demonstration Metalogic Oriel Noetics Common sense vs. Traditional logic Syllogism as a form of induction (Mill) Induction as a form of Syllogism (Whately) Quaestio or how ambiguity in inferences is resolved Informations / Instruction distinction
Richard Whately published Elements of Logic in 1826
Richard Whately’s defense of the syllogistic logic is said to be the definite defense the subject received in Great Britain. This is an essay that explores the historical context that lead up to the defense of Richard Whately of the Aristotelian syllogism. Along the way, various competing logics of the time and the dichotomy of induction / deduction is explored at good length.
Richard Whately’s work sparked a revival of logic in Britain culminating in several distinct developments. This laid the foundation for the developments by providing a spirited defense of the syllogism and of deductive reasoning generally.
Chapter 1:
Criticisms and responses from 17th century to 19th century, on the nature of logic and the epistemic utility of syllogistic reasoning, and axiomatic treatment given logic in the textbooks of the time.
Bacon’s inductive logic Descartes’ method of analysis Port-Royal logic Locke’s criticisms 18th century British textbooks in logic (Aldrich, Watts, and Duncan) Inductivist attack on logic (Reid, Kames, and Campbell) Some works (Tatham, Beattie, Scott, and Barron) Stewart’s inductive logic
Chapter 2:
Various defenses of traditional logic made in Britain before 1823 Developments in Scotland (Monboddo, Gillies, and Jardine) Ireland (Murray’s logic with Walker’s commentary, and Kirwan’s logic) England (logic at Oxford, Copleston’s defense against Kett’s text and against the criticisms of Playfair and Drummond) Lyall’s defense against Stewart Hill’s commentary on Aldrich
Chapter 3: Whately’s defense of syllogistic logic Reaction of his contemporaries Assesses Whately’s place in the history of logic In what sense Whately is entitled to be considered the reviver of logic in Great Britain
Preface
The dissertation began on the theme genesis of Boolean logic. It was supposed to have two sections: One treating the 19th century revival of logic from the time of Whately to Boole and the other dealing with trends in British mathematics which contributed to Boole’s unique outlook on logic. While on the research for the first part, the author became increasingly aware of the dearth and inadequacy of secondary accounts of developments in logic prior to Boole’s work.
The period of time under consideration: 17th through 19th century is said to be historically and philosophical fascinating though barren as far as technical developments in logic is concerned. This characterization of the setting is evidenced as perhaps causing the relative neglect with which Mathematical Analysis of Logic (1847) and Laws of Thought (1854) were said to be received in its time.
Professor John Corcoran is thanked in the preface.
History of logic is said to be more than a chronicle of its advances and the retrogressive developments of this period are also said to be important. Historical records is said to have ignored this period as in I. M. Bochenski 1970 and W & M Kneale 1692. W S Howell’s 1971 is said to be an exception, but the author records that he has a strong bias against deductive logic which Jongsma thinks, seems to have imbibed from the critics whose work is summarized.
There were any precedents that attacked Aristotle’s triumphant logic of the time.
- Bacon intended to replace the logical Organon of Aristotle with his own New Organon (1620)
- Viète challenged Aristotle’s Analytics as well as the Euclidean mode of doing mathematics in his Introduction to the Analytical Art (1591)
- Descartes opposed Aristotle’s analytics with his own method of analysis as expounded both in Rules for the Direction of the Mind (~1628) and in Discourse on the Method of Rightly Conducting the Reason and Seeking for Truth in the Sciences (1637)
— Dugald Stewart (1814) — Elements of the Philosophy of the Human Mind
Inductive or experimental science and analytic mathematics are not intrinsically opposed to deductive logic, but its outlined that there was a certain conflict owing to the methodological procedures adopted during the time which saw Aristotle’s logic as opposed to empiricist style of induction and demonstration.
Cogency and validity of various criticisms arrayed against Aristotelian logic is examined.
Criticisms of Aristotelian logic fall into two main groups:
- Those which relate to the scope and utility of logic
- Those which deal with the axiomatic organization of logic as a theory
A syllogism is discourse in which certain things when stated, something other than what is stated follows of necessity from their being so.
Aristotle does not explicitly restrict his premise set to two premises, a syllogism was commonly taken to be a pair of premises with a conclusion that follows logically from them.
But as time progressed and education in Aristotelian logic continued, by 17th century, syllogistic reasoning came to be identified as particular formulations of a simple argument – those expressly given in some figure and mood — though “syllogism” in Aristotle’s sense extends to any valid argument whatever.
When presenting a syllogism, nothing is said or implied about the truth or falsehood of the premises alone. With two premises, TT, TF, FT, FF are possibilities for the truth value of the premises. Likewise, nothing is said regarding the truth value of the conclusion, it too may be true or false. What is said, is about the relation of the truth-values of the premises to that of the conclusion. If all premises are true, the conclusion is also true. The conclusion of a syllogism necessarily follows regardless of the truth-values of the premises. This could be (can I write is here?) by the virtue of the structure in which things are related.
The conceptual structure here seems to be:
Apprehension Proposition Judgement
Where proposition consists of Subject, Predicate, and Logos. Subject and Predicates form Terms There is copula which connects between subject and predicate.
Relation between propositions is what leads to the syllogistic. It can be thought of as a propositional network or a network of relations between propositions which leads to a novel combination.
Premises and conclusion are all true in what Aristotle called “demonstration”. A demonstration must also result in a deduction to produce scientific knowledge. This is said to be not relative to any man (which means that the knowledge is objective). Demonstrations are based upon first principles which are known without deductive proof. These principles are said to be gained by sense-perception and experienced through a process of induction (epagoge / apagoge?) and are grasped to be true by Nous (intuition).
In the critique of syllogistic reasoning, it is usually not of deductive reasoning as many of the critiques share with Aristotle a deductive view of knowledge/science, but of reasoning which proceeds by means of the various syllogistic forms. They deny that, the various syllogistic forms which logicians identify and into which they analyze all conclusive reasoning, are appropriate or adequate for the tasks of deducing and demonstrating conclusions. Frege, Russell, De Morgan, and Peirce have found the syllogisms and the four Aristotelian forms of propositions (A, E, I, O) to be inadequate for formulating actual propositions and deductions. Except for Thomas Reid, the critiques accepted the claim that all reasoning can be put into syllogistic form. So their complaints are said to be about what they saw as epistemic deficiencies of the syllogism.
Three types of criticisms on the inutility of syllogism
I. 1. i. Syllogism is not needed in normal situations I. 1. ii. Syllogistic logic is not to be used I. 1. ii. 1. Does not help in uncovering new knowledge about the world I. 1. ii. 2. It is inappropriate for communicating scientific results I. 1. ii. 3. Syllogism as opposed to scientific spirit of inquiry I. 1. iii. On the epistemological structure of syllogism
- Fallacy of undue assumptions
- Petitio Principii
Criticism: Mathematicians do not formulate their arguments in syllogistic form, not even in organizing their results synthetically as in geometry. Nor do scientists use the syllogisms to arrive at knowledge of the nature of things. It is good only for academic disputation in the schools which is of highly dubious value.
Defense: Syllogisms are not prescriptions for how people ought to reason, but they are said to be forms into which any reasoning can be cast if it is to have conclusive force. Thus if there is a disagreement about the legitimacy of a given argument, it should be analyzed into its syllogistic components and then it will be clear what all the premises of the arguments are. This will help one to determine whether the argument is valid.
1. I. 1. ii: Syllogistic not to be used as is both a waste of time and a positive detriment to obtaining true knowledge of the world
There are at least 3-4 closely connected reasons given for this by the opponents of the syllogism.
1. I. 1. ii. 1. Syllogistic reasoning and disputation do not help to discover new results about the world and do not advance human knowledge.
Criticism: As methodical discovery or investigation had become a major pre-occupation with the rise of modern science in this period, syllogistic logic was seen as largely irrelevant. Some oppose syllogism by saying that induction deals with things and events while the syllogism only deals with words and thus lacks a touchstone for truthfulness. Induction begins with experiences and advances gradually to general propositions, while the syllogism proceeds in the reverse direction. They feel that the method of analysis is the true method of scientific discovery. They note that syllogistic demonstration requires a priori knowledge of all the pertinent ideas and conceptual relationships. This they believe is discovered by analysis.
Defense: Syllogism does lead to new knowledge about the world. Given the first principles, syllogism unfolds their consequences and in this sense is an instrument of science. Defenders admit by and large that syllogism is not the sole instrument for acquiring knowledge. Some other means is necessary for acquiring first principles. One can accept an inductive or an intuitive basis for the first principles of knowledge without throwing out the syllogism. The syllogism only comes into play in the process of demonstration once first principles have been determined. That this reasoning is done in words is no drawback whatsoever, for words stand for ideas or things and the truth of propositions can be checked by referring to them.
Criticism: It is often inappropriate for communicating scientific results. It is often better to present truths as they have been found rather than in a deductive fashion. Also, it is found to be too artificial a mode of deduction.
Defense: For communicating knowledge, the defenders don’t deny that results are sometimes best communicated by other means. However as a result is usually discovered through some heuristic means, communicating this process in a series of propositions cannot count as a strict deduction or demonstration. To prove to someone that a proposition is true, a deduction from accepted principles must be presented.
Criticism: Syllogistic form of argument is epitomized in the disputations of the universities. Here men defend theses regardless of whether it is true or if they believe it. Logic is employed in rhetoric to defend them. Logical training thus instills in them several notions which are downright harmful to the spirit and outlook of true science. It is said that they learn that silencing one’s opponent or gaining victory in disputation is the ultimate goal of reasoning rather than establishing the truth. This is often accomplished by means of subtle equivocation or some other piece of sophistry. These tactics thus cast a shadow on syllogistic forms of reasoning and made them suspect.
More often, acquiring the truth about a matter is hampered by faulty conception and prejudice, which make men incapable of arriving at correct principles from which to reason deductively. Syllogistic logic and disputation is said to offer little or nothing by way of correcting these faults since they are concerned merely with the forms of argumentation.
What is really needed for the purpose of obtaining true knowledge or science is a logic which directs the mind in the pursuit of truth, a logic in which rules guide one to accept truth and reject falsehood.
Defense: Proponents of syllogism are not completely agreed on the merits of disputation. Most feel it is good exercise in reasoning and should be continued perhaps in the English language instead of the traditional Latin, but others feel little will be lost to logic by dropping it.
The various forms of the syllogism were invented and continue to put an end to contentious and sophistic argumentation. So while critics of logic may have had a legitimate complaint regarding disputation as it was actually practiced in their day and earlier, they certainly threw out the good with the bad in rejecting syllogistic reasoning.
This criticism surfaces only about 1775 in Scotland.
It is claimed that syllogisms proceeds in a direction reverse to induction.
Induction proceeds from a knowledge of a particular, analogous result to a general proposition encompassing them all. Syllogisms begins with a general proposition and passes to a more particular one. It is thus diametrically opposed to its epistemic direction to the inductive produce used in arriving at general laws or universal propositions.
Aristotle’s dictum de omni et nullo is taken up by them as the basic principle underlying the many forms of the syllogism. It can be stated in various ways, one of which goes as follows: “anything which is affirmed or denied of an entire class of things can likewise be affirmed or denied of any subclass”.
As this captures the most basic form of syllogistic inference, the critics say, one can see that the original, more general assertion, which is one of the premises, must already “contain” the conclusion. The conclusion of a syllogism is thus not really new. Moreover, any inductive evidence which is sufficient to establish the containing premise would be more than adequate to establish the particular proposition. The conclusion is therefore more certain, better known, and known prior to the premises which are taken to demonstrate it. Hence the syllogistic form of reasoning is no good for demonstration.
TODO: Think a concrete instance of such a case where the inductive hypothesis becomes stronger than deductive one is needed here.
Criticism: This is said to qualify as a fallacy which is called “the fallacy of undue assumption of premises”: proving a proposition by means of another one which itself stands just as much or more in need of proof.
There’s a distinction made by Jongsma between the critiques that accuse the syllogism rather than syllogism-as-demonstration of being fallacious. Syllogism as a mechanism for establishing validity of a priori knowledge vs. demonstrating a posteriori knowledge is what is elucidated here I think.
These criticism can be countered by saying that when the syllogism is used for some purpose other than demonstration for example to determine what the consequences of a set of premises are — it cannot be accused of being a petitio principii, for no proof is intended and the premise are granted at the outset for the sake of the deduction. This point is first said to be made clear by Augustus De Morgan in Formal Logic: or the Calculus of Inference, Necessary, and Probable (1847, Page 255) and H L Mansel in Preface and Introduction in Artis Logicae Rudimenta, from the text of Aldrich; with Notes and marginal References (1862)
Taking these criticisms as applying to syllogism-as-demonstration is actually somewhat problematic, however, given Aristotle’s definition of demonstration. For the criticisms were formulated particularly with respect to knowledge that is empirically grounded. Such knowledge is obtained by induction and is not absolutely certain, as these critics admit. Therefore, strictly speaking, no demonstration is achievable here, for the premises are not known to be true. However it was generally held around this time and earlier that while such conclusions could not be known to be true with absolute certainty, they were to be regarded as certain for all practical purposes, at least until contradicted by fact.
A problem remains, though. What criteria might such demonstrations be expected to conform to? Here too there is a divergence from Aristotle.
Aristotle begins with premises that are better known than and prior to the conclusion. He explicitly pointed out that he meant this in an absolute sense, not in a sense relative to man. An argument that is based on premises which are better known or known prior to man is no demonstration at all. Such premises, being closer to sensory perception, cannot provide the true explanation or cause of the consequence. To know something requires recognizing the universal in the particular.
On the reversal of order of knowledge between Aristotle and Empiricists: An Aristotelian way out of the conundrum
Both Aristotle and the modern, 17th and 18th century critics of logic appear to hold in common that there is a fixed order of knowledge, that one can only truly know something if one knows that it is so, based on some earlier (epistemologically prior) knowledge.
Aristotle holds that one can attain a knowledge of primary truths and these are better known than all other truths, which must then be demonstratively based upon them in order to be known.
First principles -> demonstration -> natural knowledge
The modern inductivists hold that axioms or first principles are the last thing one knows and that other truths are obtained in the process of coming to know them.
Natural knowledge -> induction -> First principles
In the realm of mathematics: First principles <- demonstration, induction -> Mathematical Knowledge
In the realm of mathematics, this might not lead to any conflict, for mathematical axioms might be considered prior both in an absolute, Aristotelian sense and in a modern, relativized sense. But in the realm of natural knowledge about the world a conflict between the two does appear.
Out of their empiricist or inductivist view of knowledge and their analysis of the structure of the syllogism, the eighteenth and nineteenth century critics of Aristotelian logic reject the syllogism for failing to meet their criteria of a true demonstration: relative to a knower a syllogism’s conclusion is always better known and known prior to the premises. Their criticisms that the syllogism is fallacious, therefore, are claims relative to their new notion of demonstration, which is tied to their order of knowledge.
This reversal means that the concepts of demonstration and knowledge now have different meaning. A demonstration proceeding in this new sense, one might maintain, would be worthless to science, for it would not proceed from cause to effect but from effects to their causes.
Effects -> induction -> Causes
The order of knowledge needed by science is precisely that laid out by Aristotle. How would demonstration, in the new sense of proceeding from facts better known and known prior to man be any different from the induction process? Also what is one to do with the general proposition attained through induction if not reason from them?
So if the syllogism is epistemically faulty or a petitio principii in a certain domain, all valid arguments there are likewise, for no premises are added or changed when an argument is transformed into a series of syllogisms.
The defenders of the syllogisms did not take the Aristotelian way out which is sketched. They approached the issue from the opposite side instead, relativizing the notion of “knowledge” and “demonstration” even further. Rather than defining demonstration or proof in terms of knowledge relative to man in general, they defined it in terms of an individual person’s knowledge.
The responses given to these accusations lie on 2 levels.
Which does not explain why the syllogism is not fallacious, but which does argue that it can’t be so.
Here the defenders note that if the syllogism is fallacious, then so is demonstrative reasoning of any type, since the syllogisms is only the regular, expanded form of all demonstration.
Ad hominem argument as having an old non-perjorative sense is outlined.
This kind of ad hominem is then advanced against the critiques of syllogisms. They isolate and syllogistically formulate the argument charging the syllogism with being fallacious and then, on the critic’s own principles, accuse of it being a fallacy and no demonstration of the syllogism’s inutility.
The defenders say that it is wrong to oppose induction and syllogism, for they belong to quite different parts of the epistemic process and they achieve different ends. Induction is a process of inquiry; it is not a type of rational discourse alongside of the syllogism. Were it to be put into a valid form of reasoning, they say, it too would be syllogistic. As such, it would require a more general induction principle as a premise in order to derive the inductive conclusion and thus would no longer pass just from particular results to a more general one. It is best, thought, to see induction and syllogistic reasoning as complementing one another, the syllogism taking up where inductive investigation leaves off.
In discussing the structure of the Aristotelian dictum, the defenders accept the assertion that the premises of a syllogism contain the conclusion in implicit form. A consequence, they say, may even be considered to be contained in one of the premises, but the other premise is required to exhibit this fact. In explaining why this view does not entail the epistemic futility of the syllogism (or of deductive reasoning generally) the promoters of syllogistic reasoning are a bit pressed to come up with a completely convincing reply.
M A E Dummet 1975: The Justification of Deduction: https://philpapers.org/rec/DUMTJO
J Woods and D Walton 1975: Petitio Principii: https://www.jstor.org/stable/20115058?seq=1
There seems to be the idea of syntax/semantics justification playing out here. Especially in the work of Susaan Hack: https://exitingthecave2.wordpress.com/2017/04/30/haack-and-dummett-on-the-justification-of-deduction/
They agree that a syllogisms does not infer an absolutely new conclusion, that is, one not implicitly contained in the premises; otherwise the argument would lack conclusive power. One who accepts the premises of a syllogism is forced to accept their consequences as well. One may know the premises without knowing all they entail; the syllogism makes it evident that the result is so contained or implied in the premises.
A distinction to make in this context is among: a valid argument, a deduction, and a proof.
An argument is valid if the conclusion follows logically from the premises A deduction is a special type of valid argument, one in which the consequence is shown strictly to follow according to the stipulated rules of inference A proof is a deduction which has among other things, premises that are known to be true
I think this spawns a typification where by proof is a subtype of a deduction is a subtype of valid argument.
Whether an argument is a deduction depends upon what the primitive rules of inference are. If each step in an argument is either a premise or is obtained from the premises by means of a primitive rule of inference, then it is a deduction. A valid argument may have deductive gaps, but a deduction or a proof cannot.
In this manner, a valid argument which is not a strict deduction or proof is an argument, then, whose premises logically contain their consequence but which does not make evident that the conclusion follows from the premises.
Examples of knowing Euclidean geometry or of Archimedes’ mechanics is and yet not knowing the Pythagorean theorem or the law of the lever is given.
I am not sure that valid arguments with deductive gaps map on to Pythagorean theorem, which I think can be obtained by deduction. I think what needs to be emphasized here is the idea that when the analytical trees are drawn out, the logical implications could be far removed from the premises and can create really complex structures where the conclusions could be surprising results from the axiomatic premises that are set up.
Problems with syllogistic reasoning cannot be blamed on the fact that premises imply or contain their consequences. The inutilitiy of syllogistic reasoning throughout a given universe of discourse must therefore relate either more particularly to the syllogistic form of the reasoning or simply to primitive deductions.
There is an opportunity here to locate the inutilitiy of the syllogism in syllogisms’s particularizing a premise to obtain a conclusion. But if it is to be held simultaneously that epistemically useful demonstrations do exist (perhaps arguments in which the relation between premises and conclusion is implication or containment in some sense, but not particularization), then the view that all deductive reasoning can be put into a syllogistic mold is to be relinquished. This is hardly contemplated by any of the critics. (It is not entirely clear how particularization is different from implication part)
It is possible to distinguish valid arguments from deductions even in the case of single, unlinked syllogisms. Aristotle seems to have done just this in distinguishing a certain class of syllogisms as “perfect”. This can be seen in:
Aristotle’s Natural Deduction System — J. Corcoran 1974, 92 The Contemporary Relevance of Ancient Logical Theory — J Corcoran and M Scanlan January 1982, 79-81
A perfect syllogism, for Aristotle, is one in which no further propositions are needed in order to show that the conclusion follows. Such are all first figure syllogisms.
A syllogism is imperfect if it is a syllogisms which requires additional propositions (still based on the given premises, of course) to make the conclusion evident. An imperfect syllogism can be made perfect by interposing new propositions which follow directly from the argument’s premises until no gaps remain.
I think this characterization is where the gaps become explicit instead of tacit. I have to study probably the Corcoran paper to make sense of how this is different from the reduction procedure.
Taking as the basic rules of inference the Aristotelian dictum (or the first figure moods) plus certain rules of conversion, the various moods of the syllogisms can be completed or deduced. In this way imperfect syllogisms are converted into deductions.
The notion of imperfect syllogisms being deduced is said to have dropped out of the logician’s repertoire by the modern era. In its place was a theory of reduction procedure, where the various syllogistic forms can be reduced to first figures.
Reduction is accomplished, roughly speaking, by transforming the premises of a syllogism until a first figure configuration is obtained which can be used to deduce the conclusion.
So while non-first figure moods were taken to be less primary in some sense than the first figure moods, they were on a level with them with respect to deducing conclusions. This framework would have made it difficult for logicians to distinguish between two classes of logical argumentation with respect to the single syllogism. The best that could be done here is to do approximately what Whately did — assert that some syllogistic forms applied to some premises make evident or yield new knowledge of a sort to certain people.
Now coming to responses that were actually made, the following arguments were given by Whately and others around 1825.
Relative to an individual person’s state of knowledge, a syllogism may indeed generate new knowledge. For a given person, a particular syllogism will function as a proof of its conclusion if it proceeds from premises better known and known prior to him, though it may not count as one for someone else. By combining one premise with another, one could discover or bring to light a result that was (as they thought) already contained in that other one.
Particularly in the mathematical sciences, deductive reasoning uncovers new knowledge for everyone. Prior to a result’s being proved it is still a conjecture; it only becomes knowledge when it is deduced from more elementary propositions.
The defenders of syllogistic reasoning were not completely clear how this could be so, given that the premises contain their consequences, but the fact that it was so was clearly stated.
These answers did not completely satisfy everyone. The critics may have felt that something of a swindle was taking place by relativizing knowledge further, by being too loose about what counts as knowledge.
Just when does one know a proposition? If a given universal proposition can only be gotten in the first instance through an empirical process of induction, one must arrive at the knowledge of that result by passing through various stages of generalization. Does not such a person know then, the particularizations of that proposition to the various stages and individual objects? Is not the universal proposition merely a compact way of asserting that each individual or species of individual contained under the subject jointly with every other individual does or does not have a certain property? In asserting such a proposition, then, does not one really already know all the consequences which can be deduced from it via a syllogism?
In empirical induction, one goes progressively from the particulars to the universals. When one undergoes such a process, aren’t they already familiar with the particulars they have generalized?
Reply to this was given by Mansel who was more sympathetic to a Kantian philosophy of knowledge than an empiricist one.
Mansel notes: an empirical induction is usually not complete is not obtained merely by considering a set of individuals and generalizing to a larger class
Hence, one cannot consider all the particularizations of the inductive conclusion to count as evidence for the conclusion. Nor, already known in asserting it, even if the proposition is thought of as including it. Therefore it is quite in order to infer a conclusion from this premise regarding a case not previously investigated. The resulting proposition will yield, strictly speaking, new knowledge.
This I think means that there could be particularizations of the general class which weren’t encountered when inducting upwards.
Criticism: A second criticism of the syllogism which historically comes out of this one is the related charge that the syllogism is in essence a petitio principii.
Aristotle defines petitio principii / begging the question to be a fallacy of demonstration in which one somehow attempts to prove a proposition by means of itself, either immediately (by assuming the conclusion as a premise, usually covertly) or indirectly (by assuming as premise a proposition which requires the conclusion in order to demonstrate its truth). Begging the question thus yields circular reasoning (or an “arc” of the circle) within the realm of demonstration.
The petitio charge is a distinct intensification of the accusation that it is a fallacy of undue assumption, claiming as it does that a definite epistemic and logical relation holds between the “containing” premise and the conclusion. It is made by the critics of the syllogism, however, pretty much on the basis of the above analysis of the epistemic structure of the syllogism, not on a new analysis or any additional evidence.
The syllogism is considered as a petitio principii for the truth of the premise presupposes that of its consequence.
Response: If an argument is a petitio principii, it makes use of a premise that, in the order of knowledge (whether taken as absolute, relative, or individual) is logically posterior to the conclusion; that is, in order to prove the premises from what is already known, one must make use of the conclusion somewhere along the line. For the syllogism to be a petition principii in this sense, then, one would have to show that the conclusion of any syllogistic demonstration is logically necessary for a proof of one of the premises.
For the conclusion to be a necessary principle underlying the premise in question, one would at the very least have to exhibit a proof in which the conclusion functions as a premise.
I think the author here means that the premise is predicated upon the conclusion, or premise is a function of the conclusion, that is f(conclusion) = premise in some manner. In this sense, there’s a circularity established.
Suppose that a universal proposition with all objects of a given class have a certain property is gotten by an inductive generalization after a careful investigation of a supposedly representative sample of these objects.
{diamond, queen}, {hearts, queen} All queens are red.
For each instance or subclass of this class, one could form a syllogism which takes the universal proposition as its major premise and which has as its conclusion the assertion that this instance or class of instances has the said property.
Some of these conclusions would state (partial) evidence on which the universal proposition was originally asserted, others would not. Now if we use them as propositions on which one could demonstrate the major premise — that is, if the syllogism is a petitio principii — it should be possible to give a strict proof the inductive generalization which depends basically on these particular propositions. This amounts to being able to deductively justify an inductive generalization, drawing only upon those propositions actually known to be true. Such a program is said to be impossible.
I would have to provide an instance of this case and analyze how far an inductive generalization can be evidenced from a deduction.
This is not what the critics seem to have intended. What they seem to have meant is instead roughly the epistemological counterpart of the description. Can I say that, it’s not the structure, but the content of these structures that was the point of contention?
The knowledge of the premise includes or presupposes that of the conclusion: what is parading as a proof, therefore, is no proof at all, for the conclusion is actually epistemically prior to one of the premises.
This criticism is said to have vague terminology and is said to have persisted into 20th century text in such texts as M R Cohen and E Nagel (An Introduction to Logic and Scientific Method (1934))
The premises contain the conclusion only means that the conclusion can be logically derived from the premises. It does not necessarily mean that knowing the premises necessitates knowing the conclusion too, at least not before the proof is derived. The truth of the conclusion being presupposed by the premises is a way of asserting the logical connection between the premises and conclusion. If the premises are true, the conclusion must also be true. If one accepts the premises, he commits himself to the conclusion as well.
Jongsma describes that there could be particular syllogism that does beg the question, in which case it doesn’t become a valid demonstration. For the critics to assert that this happens universally, they would have argue the difficult thesis that no universal proposition can be known except through knowing all its instances. Something like this is said to not be reflect much until Mill’s 1843 logic.
I have to think how bringing in the syntactical/semantical distinction about various deductions would weigh in here. Would it help clarify how one commits to a syntactical sort of deduction? I would probably have to read Susaan’s and Dummet’s articles before proceeding. Jongsma hasn’t introduced such terminology into this text so far.
In the aftermath of these events, syllogistic logic was ignored or even rejected in the late 17th and 18th centuries in favor of a more practical, epistemologically oriented analogue. A de-emphasis on reasoning plus homiletic cautions to use only clear and distinct ideas, to strive to overcome prejudice, and to avoid equivocation characterizes this approach to logic.
There were thoughts in this period on both sides of the knower on how mental operations actually produce knowledge and the known on how various types of evidence which attach to propositions. Logicians of this period consciously expanded logic with respect to reasoning by incorporating discussions on types of reasoning which are not strictly conclusive or deductive.
Advocates of Aristotelian logic reassert that the logic is only concerned with forms of thought and forms of reasoning and not with particular content or meaning. The view of logic which sees it as a/the practical art for guiding one in every field of thinking in order to arrive at truth and avoid falsehood is absurd. By making such an unreasonable demand, men are naturally led to turn away from syllogistic logic. Logic is only concerned with valid arguments, and these, when stated in standard form, are necessarily syllogistic.
The subject matter of logic is redefined and its scope is narrowed by the defenders of logic to delimit it from philosophy of mind. Epistemological and metaphysical concerns, they assert, do not belong in logic. While they regard mental philosophy as a legitimate field of study, combining it indiscriminately with formal logic usually results in confusion and to its wrong depreciation. Logic is concerned with reasoning and the subsidiary mental operations of apprehension and judgement. And they add it is only concerned with these insofar as it deals with the conceptual results of these operations with ideas, judgements, and arguments (terms, propositions, and syllogisms).
Logics of the time, other than Aristotle, treated the theory of the syllogism as an axiomatic science like Euclidean geometry. Axioms were laid down at the outset and various results were proved by means of them.
Fundamental principles are of two types: Valid and invalid ones.
On the basis of certain axioms or canons, various rules are proved which all valid syllogistic moods are required to satisfy. Arguments which violate any one of these rules are rejected as invalid. The remaining argument forms are valid, though they are not established as such by this procedure.
Aristotle rejects syllogistic moods as invalid by giving counter examples. This process is said to not be as economic as the method described, but is said not to suffer from the faults of this economic method.
It is noted that rejecting invalid moods does not amount to establishing validity for the rest and this mistake is said to have happened in Cohen and Nagel text. Rejecting invalid moods does not amount to establishing validity for the rest. This is same as lacking a proof of the parallel postulate in geometry shows it to be independent.
Even if one did have a proof which showed that the remaining moods could not be rejected on the basis of the given rules, that still does not mean that they are valid, unless it is also known that every invalid mood must violate one of the rules given (or equivalently, that any argument-form which does not violate one of the rules is valid). Absence of negative evidence regarding the moods’ validity cannot otherwise be construed as the presence of positive evidence that they are valid.
The opponents of logic’s main criticism of the invalidity procedures relates to the principles on which it rests. They scoff at rejecting invalid moods en masse by means of rules instead of considering the moods individually as Aristotle had done, but given the approach, they still question the appropriateness of assuming as axiomatic the principles which are posited.
The issue of which principles are proper and sufficient on which to base logic remained an important topic of discussion among logicians in 19th century Britain. The criticism regarding the use of rules for rejecting invalid moods seems to have gone almost unheeded.
Whately says that using axiomatic rules to demonstrate invalidity is easier, requires less ingenuity, and is more scientific than using counter-instances.
Validity for syllogisms can be proved directly for all moods on the basis of two methods, each of which can be done in two ways.
- General principles approach
a. By giving a set of principles which apply to all moods irrespective of figure (such as Port-Royal principle of containment) b. By giving for each figure a principle which establishes the valid moods in that configuration
- It can be proved of certain distinguished moods (some or all of first figure moods) and these can then be used to establish the validity of the rest
a. After deriving the distinguished moods directly from the given axiom (usually Aristotelian dictum), one can use them to deduce the remaining ones b. One can reduce the other moods to the distinguished moods by appropriately transforming the premises and conclusion
The reduction process demonstrates the validity of the syllogism; or as they are fond of putting it, it demonstrates demonstration.
The failure to distinguish between syllogistic arguments that make their conclusions evident because they are deductions and those which are valid but not evidently so resulted in ridiculing the reduction process as that process was a further step to establish validity. This is tied in with the loss in distinction between perfect and imperfect syllogisms in the original Aristotelian canon.
Whately and proponents of the logic say that reduction does not demonstrate an argument’s validity. They agree on the whole with the critics that it is absurd to demonstrate that a syllogism is conclusive. Whately argues that the demonstration only shows the basic principle on which all reasoning proceeds, namely, the Aristotelian dictum; that it accounts for the validity of the moods though it doesn’t prove them or make them more conclusive. William Hamilton said that the process of reduction shows why the syllogistic forms are valid, but it does not demonstrate that they are valid.
The confusion might have been dispelled if the participants recognized that proving a syllogistic form to be valid does not make it valid, it only makes evident why and that it (the evidence probably) is valid. The defenders were correct in rejecting the belief that the reduction process added conclusiveness to the argument forms, but they were wrong in thinking that syllogistic forms cannot be demonstrated to be valid.
Bacon criticized Aristotle’s logic. He said that deductive reasoning operates on concepts and propositions already given to it and so tends to perpetrate error and falsehood rather than challenge it. This way of philosophizing is bound to results that follow from those assumed at the outset.
Syllogistic logic deals with words and notions and propositions; it does not aim at investigating things and their interrelationships. It commands assent therefore to the propositions, but does not take hold of the things.
Bacon notes that logicians tend to make premature abstractions and hasty judgements, to accept general axioms and definitions without adequate investigation, and to derive particular results from general principles instead of from an analysis of the relevant things and events. Ancient and scholastic philosophers err or precisely these counts, using categories which do not conform to the nature of things and adopting as first principles propositions which have not been sufficiently established by experience. Proceeding from there to deduce specific consequences by means of syllogistic reasoning, their systems remain closed to any correction from nature itself.
Because results are deduced from axioms and definitions that are taken as indubitable, these systems are mistakenly considered unassailable by their promoters. However, a deductive system is only as good and as complete as its collection of definitions and axioms or first principles, and so must be judged by things external to the system itself.
One must be extremely wary of reducing scientific knowledge to a method or art, since then the focus of one’s concern becomes the organization of known material rather than the continued growth of the field through accumulated observations and new inductions.
Although there are indeed a number of passages in which Bacon extols the use of the (deductive) method.
Bacon distinguishes between enumerative induction and his brand of induction.
Enumerative induction is that procedure which draws a universal conclusion on the basis of the proposition being known true for a number of particular instances. This is often called logical induction or complete induction. If these instances are known to exhaust the total possible cases, the conclusion is rigorously demonstrated, but such a situation hardly, if ever, occurs in empirical investigations and is usually trivial in application. On the other hand, if the induction is based on a partial survey of instances, the conclusion has not been proved true. Bacon scoffs at incomplete form of induction as “conjecture”.
According to Bacon’s view, one should ascend gradually and cautiously from a thorough knowledge of particulars to notions and propositions, and from them to even broader concepts and axioms, until finally the most general principles are obtained.
Bacon structures caution into his inductive method in a way that distinguishes it from the enumerative forms of induction. When one wishes to draw a conclusion about the cause or true nature of a certain type of phenomenon, he begins by constructing a table giving the “history” of the phenomenon. This table lists a large number of events relevant to the phenomenon, events in which the phenomenon occurs while its potential causes do or do not occur, and, if the phenomenon and its possible causes can be present in varying degrees of magnitude, events in which these different degrees occur.
| Causes / Nature which occur | Phenomenon does not |
| Causes / Nature which do not occur | Phenomenon does |
| Causes / Nature which occur / whose degree of variation is improperly reflected in the phenomenon | Phenomenon does |
There seems to be a repetition in the statement in the text on correlating appearance/disappearance of causes and phenomenon. I am interpreting this as { Does / Does not, Does not / Does, Does Does } for now. { Does not / Does not } probably isn’t relevant to the analysis I’m assuming (which could be wrong depending on the method intended)
After excluding those causes or natures which do not account for the phenomenon, one will ideally be left with the true cause or nature of the phenomenon. Augustus De Morgan attributes Bacon’s view of inductive procedure to his legal training. There one suspends judgement till all the facts are in.
Naturally, as Bacon realizes, this presumes that all possible causes or natures have been determined; otherwise one might conceivably end up excluding all causes thought to be relevant. Bacon’s inductive method, therefore, consists of two main parts — an exhaustive analysis, and a process of exclusion.
Assuming that nature can be completely decomposed into its primary or elementary natures or causes, and that full tables can be constructed for any given phenomenon, Bacon’s method of induction or exclusion is, as he conceives it, a method of “proof”. By means of it, one can establish or “demonstrate” the first principles (as well as principles of intermediate generality) of any science.
The importance of this assumption in Bacon’s thought is pointed out by Henry Hallam in his 1837-9 work on the literature of Europe and by Robert Leslie Ellis in the preface to Bacon’s philosophical works. Francis Bacon, A Critical History of Western Philosophy — M Hesse 1970 is also referred for comparison.
- Bacon thinks induction arrives at absolutely certain conclusions. In this regard, Bacon is aligned with Aristotle who held that it was by means of a such an induction process that axioms or first principles were obtained for science, and these were, of course, true and absolutely certain.
Bacon’s followers however evidently abandoned the ideal of completely analyzing nature into its basic components as unattainable or perhaps illusory, take Baconian induction to be merely a careful variety of ordinary induction, yielding only probable results, even if quite trustworthy or “morally” certain. See The Problem of Certainty in English Thought 1630 – 1690, H G Van Leeuwen 1963, and also Studies in the Logic of Theory Assessment in Early Victorian Britain 1830 – 1860, J V Strong (1979)
- Bacon’s view of induction is that it is a process of proof/demonstration. It is said that by using demonstration and proof to cover both of these different procedures, Bacon blurs categories and this enables him to go on to oppose induction and syllogistic reasoning as if they lie on the same plane. This confusion was unraveled by Copleston and Whately who inexplicably exonerate Bacon of the opposition and lay the blame on his latter-day adherents.
In this Bacon parts company with Aristotle. Aristotle held that first principles are established by induction, not demonstrated by it. Demonstration is for him a process of showing a proposition to be true on the basis of other propositions already known to be true. Induction, for Aristotle, leads from experience to first principles (a purely epistemic, non-discursive process). Demonstration proceeds from these propositions to others based on them (a logical process for an epistemic purpose — the extension of knowledge).
Bacon’s new organon, his logic of induction, is placed in opposition to Aristotle’s work not just because of the diametrically opposite structures of induction and deduction, but more importantly because induction is a method of proving propositions which are usually proved syllogistically.
Bacon claims induction has edge over the syllogism because it is empirically based and deals with reality, while the syllogism remains locked within the domain of words and propositions, where deception more easily arises. He also thinks it has advantage over syllogism because it can be used to discover and prove first principles, while syllogistic reasoning must merely take them for granted, there being no fundamental principles from which they can be derived. So a deductive approach to knowledge, in Bacon’s view, is said to develop the wrong methodological habits for investigating nature and so should be used sparingly, if at all, in science. Bacon feels that his logic of induction is superior to syllogistic logic, and that it is so regardless of the field of knowledge under consideration. Bacon conceives his methodology to encompass the whole gambit of knowledge.
Note: I think I will have to read through Bacon’s work to understand how this sits with his idea of idols from which humans have to distance themselves. I feel that his method is deeply tied up with his philosophy.
Deductive reasoning is considered by Bacon to be useful in fields of discourse such as religion, civil law, or games of wit, where people are either required or choose to reason together about matters relative to certain given standards or “posited” propositions that are “exempted from examination of reason”, either because of the authority of the source or through mutual consent. Bacon hints that syllogistic reasoning might be of some use for convincing people of results in natural philosophy, but he immediately qualifies this by noting logic’s retarding effect on the progress of science, for one will never be able to amend false hood purely by arguments; one must appeal beyond words to the things themselves.
The complexity of the proof of a theorem might relate to how many auxiliary constructions are needed, the number of steps, and the way in which the principles are combined to net the result and so on. Jongsma notes that in mathematics such as deducing the Pythagorean theorem or the area of a circle, deduction shines. Tracing a geometrical proposition back to its ultimate principles is quite different than inductively generalizing from particular experiences to a universal proposition.
One might not know in the initial stages of developing a demonstrative science like geometry which set of propositions to take as first principles, but in choosing them one looks for principles which are elementary, both in the sense of being well known or easily knowable and being able to provide a deductive basis for the remaining, lesser known results. One does not generalize the consequences or inductively ascend from them to obtain the axioms.
E J Dijkersthuis in The Mechanization of the World Picture, M Hesse on her article on Bacon (1970), and R L Ellis evaluates Bacon’s view as having little negative value in criticizing Aristotelian philosophy that had not been said before by men such as Peter Ramus (1515 – 1572)
A re-evaluation in defense of Bacon’s philosophy of science is provided by M Horton (November 1973)
In the last quarter of the eighteenth century and the opening decades of the 19th, Bacon’s critique of Aristotelian logic was taken up by the Scottish common sense philosophers and, together with Locke’s criticisms and a few ones of their own, was made the basis of a renewed wave of attacks upon syllogistic logic.
Regulae ad Directionem Ingenii (1628, published 1701)
Discours de la méthode pour bien conduire sa raison, et chercher la verite dans les sciences (1637)
Though there’s paucity of explicit references, Descartes work can be viewed as an attempt to formulate a competing organon of knowledge to replace Aristotle’s Analytics.
Greek Mathematical Thought and the Origin of Algebra (J Klein 1968)
While Bacon had assailed logicians for failing to obtain a sound inductive base for knowledge, Descartes’ epistemological approach was highly conceptual rather than empirical. Reason was his supreme guide in human thought and action.
By methodically doubting all things, Descartes hoped to throw off all those opinions which were sanctioned merely by authority or testimony and adopt only those which could be rationally established on a deductive basis of clear and distinct ideas.
Though mind is seen as the source of certainty, it is in a definite need of a method or set of rules by which it can be properly directed in discovering the truth.
Renaissance Concepts of Method: N Gilbert 1960
The function of Descartes method differed fundamentally from the discussion of the method/order/organization/disposition at the time. He intended it not first of all for communicating or imparting truth to others, but for discovering it. Descartes’ primary concern was to fashion an art by which truth can be found, irrespective of the subject matter being investigated, a universal method of scientific inquiry.
Logic and Rhetoric in England 1500 – 1700, Wilbur Samuel (1956)
Descartes found the method of analysis present, though disguised, in the algebra of his day. Here the method was ignorantly obscured by considerations of number which restricted its scope and hid its true universality. Mathematics, as Descartes came to understand it, was the general science of order and measurement, alike applicable to number and every kind of magnitude. Its method was that of analysis and synthesis.
Method consists entirely in the order and disposition of the objects toward which our mental vision must be directed if we would find out any truth. We shall comply with it exactly if we reduce involved and obscure propositions step by step to those that are simpler, and then starting with the intuitive apprehension of all those that are absolutely simple, attempt to ascend to the knowledge of all others by precisely similar steps.
Descartes method was a composite of both analysis and synthesis.
Complex or difficult propositions are decomposed or analyzed into simple ones and these ultimately into ones that can be compared with intuitively true propositions. Propositions are intuitively true or self-evident if they are clearly and distinctly perceived to be so, if reflection upon the ideas immediately (that is, without the deductive assistance of any mediate ideas) shows the proposition to be so. When the simple propositions of first principles on a given topic have been ascertained, they can be combined to deduce more remote conclusions and so extend the circle of known truths.
Analysis for Descartes is the true method of discovery by which difficult questions can be reduced to simpler ones, the truth of which may then be decided on the basis of mental intuition. Intuition provides the fundamental truths while deduction proceeds from them to infer other truths whose connection had previously been traced out and established by analysis.
Given Descartes’ preoccupation with discovery, typical of his day, the art of analysis predominates in Descartes’ thinking about method. Synthesis or deduction is also important as part of his overall method of science, but it is not stressed to the same extend that analysis is. And unlike analysis, deduction needs no art to guide it, for men rarely make false inferences. If men are clear in their ideas and have correct premises, they will rarely err in reasoning from them.
The study of logic is therefore of little use in Descartes’ system of thought. hH admits that one may reason syllogistically on matters of opinion for mental exercise, but such a practice is certainly not appropriate for engaging in an unbiased investigation of the truth or arriving at knowledge.
Quaesitum and datum
N Gilbert claims that Descartes’ view of proof as “linear demonstration” was discussed in 16th century and derives from Galen’s ideas on geometrical method. Descartes’ ideas were enthusiastically taken up by Locke.
Descartes’ main complaint against logic is that it is unsuitable as a method of discovery. Because of its reputation as an organon of knowledge. Descartes had once pondered whether logic might be a tool of scientific investigation, but he soon concluded that it was not. He concedes that syllogistic reasoning may be used in some instance to communicate results already obtained, but he judges it absolutely useless for discovering new truths.
Descartes says that “Dialecticians are unable to devise any syllogism which has a true conclusion, unless they have first secured the material out of which to construct it, i.e. unless they have already ascertained the very truth which is deduced in that syllogism”.
To this Jongsma interprets it at face value as: “Descartes seems to be saying that one must known that premises of a syllogism are secure or true in order for the conclusion to be true.” This is false as for false premises may well yield a true conclusion, which Aristotle has stressed at length.
A more viable interpretation is taken to mean “syllogistic demonstration” rather than mere “deduction”. In this way, it is true that if the syllogism is to be a proof of the conclusion, one must know that the premises are true. This outlook is related to a petitio principii charge which was later used by George Campbell in 1776.
But this interpretation is said to be inconsistent with Descartes’ view of deductive reasoning in general. This is plausible in the case of a single syllogism, for the conclusion might seem to be about as intuitive as the premise. But as several syllogisms are linked together, it becomes a long or complex proof, which could be much further from the premises.
Here it becomes quite apparent that, on Descartes’ standpoint, syllogistic reasoning must bring about new knowledge.
The results proved may have been discovered before being deduced — the task of Descartes’ analytic method — but they are not strictly counted as knowledge until their truth is proven, that is, demonstrated from first principles.
Descartes is saying that to prove a proposition true one must first discover both the result itself and the relevant premises that will show it to be true. The rules of syllogistic logic are of no help there. This is a job for analysis, which traces a proposition back to its source, the first principles, so ascertaining it. Descartes is of course well aware that analysis must be followed up by deduction in order to prove the “truth” found. For Descartes the true logic is one that teaches us how best to direct our reason in order to discover those truths of which we are ignorant.
Descartes puts forward his own logic of discovery, the method of analysis, gleaned primarily from his study of ancient geometrical analysis and contemporary algebra, as the heir-apparent to Aristotle’s logic, the replacement for Aristotle’s organon.
Since the method of analysis was, not surprisingly, most fruitfully applied to geometry and algebra, culminating in the calculus, Descartes’ work is the historical source of the conflict between mathematical analysis and traditional logic within modern physical science.
Today, no problem is seen in having science make use of both mathematics and logic to achieve its aims, but at a time when logic was held to supply rules for directing man’s mind in his quest for true knowledge, it was bound to clash with the rising science ideal in which mathematical analysis played an increasingly large part.
For Bacon, syllogistic logic had been found inadequate for science on account of its failure to incorporate a scientific method of induction, which was supposed to be at once a method of discovery and a method of proof. With Descartes, syllogistic logic is found wanting because it fails to include a rational method of discovery and because it does not properly capture the procedure of deduction. In the work of Bacon and Descartes, therefore, the fundamental forces opposing traditional logic are set in motion. Epistemological challenges to syllogistic logic are thus laid down both from an empirical and a conceptual standpoint.
The Port-Royal Logic was written by Antoine Arnauld (1612 – 1694), the principal Jansenist theologian of the Port-Royal community, though parts of it were due to Arnauld’s colleague, Pierre Nicole (1625 – 1695).
La Logique ou l’Art de penser: contenant. outre les règles communies, plusieurs observations nouvelles propres à former le jugement
Port Royal logic is primarily known today for its distinction between the comprehension and the extension of a term (roughly between its intensional and extensional meaning). This distinction is said to be similar, though not identical, to the medieval one of signification and supposition.
It was the most important logic textbook during the 17th, 18th, and early 19th centuries considering its numerous editions (at least 25 different French editions).
Logic is the art of directing reason aright in obtaining the knowledge of things, for the instruction of ourselves and others.
Arnauld follows in Descartes’ and Bacon’s footsteps in assigning to logic an investigative and methodical role in the enterprise of scientific knowledge. Reason is to be directed by an art or system of rules, which comprise logic.
Descartes’ pervasive influence can be seen in the part on ideas, in the part on judgement, and elsewhere.
Two primary manuscript sources for Arnauld’s logic was Descartes’ unpublished Regulae, and L’Esprit géométrique of Arnauld’s Jansenist follower and defender, Blaise Pascal (1632 – 1662)
Induction is largely neglected.
“It is in this way that all our knowledge begins, since individual things present themselves to us before universals.“, yet induction can never lead to certain knowledge, unless the set of particulars examined exhausts the universal — that is, unless it is “complete induction”.
The consideration of individual things furnishes to our mind only the occasion of turning its attention to its natural ideas, according to which it judges of the truth of things in general. Investigation of particular things stimulates the mind to analyze, clarify, and interrelate the ideas which it naturally contains for thinking about such things, and it is this rational process which leads to certain and universal knowledge about the world.
Arnauld does not restrict logic to its supposed investigative function, as Descartes had, but allows it a proper role in organizing and transmitting that knowledge to others. Arnauld thus joins a Cartesian epistemology and logic of discovery to a more traditional logic of argumentation. This particular form of synthesis was detrimental to syllogistic logic, and was probably responsible in part for the further decline of interest and research in syllogistic logic.
Logic is taken to be the art of directing reason aright, not just of right reasoning. This means that he brings in the idea of logic dealing with thinking including reasoning. Logic is conversant with thinking in all its functions, according to Arnauld, not merely in its reasoning capacity to pass from premises to conclusions.
The end (goal) of logic was conceived to be giving rules for all the operations of the mind, and thus as well for simple ideas as for judgment and reasoning. Logic should not be a mechanical or purely formal art of reasoning, but an art which trains men to make true judgments on genuine issues.
Arnauld divides logic into four parts, each one associated with a distinct operation of the mind, something which became standard during the following era:
First part treats ideas or the results of the mental operation of conceiving. This is considered to be the most important part of logic, since all knowledge is by way of ideas. After Arnauld discusses and dismisses Aristotle’s 10 categories, he presents his distinction between comprehension and extension, and he expounds Descartes’ view of clear and distinct ideas. In connection with this, he also looks at how a misuse of language may introduce obscurity into human discourse, which points out the need for proper definition of terms.
Second part considers judgements and propositions, the mental and linguistic counterparts that result from the act of judging. Once having arrived at ideas of things, these ideas may be compared to see whether they “agree” or not. Those which agree may be joined together in a judgement which affirms their connection. He gives a taxonomy of different types of propositions:
affirmative/negative universal/particular/singular simple/compound/complex
This section also contains the theory of definition and a brief description of the possible logical relations holding among pairs of propositions: types of opposition and conversion of propositions are treated here.
Third part of his logic deals with reasoning and syllogism. He notes that the importance of the rules of reasoning have been greatly exaggerated. Correctly formulating ideas and making true judgements about them are at least as important, if not more so, than following forms of reasoning. Errors generally arise, in actual fact, more from a deficiency on these two counts than from a defective process of reasoning.
Reasoning is necessary, because of the limitations on our ability to judge the relationship between two ideas directly. One must often resort to a third idea with its relations to both of the other two ideas in order to mediate the connection between them. The division between judgement and reasoning is not hard and fast. Judgements often conceal reasoning within them and reasoning is an extended form of judging. The result of reasoning, the syllogism, can be formulated as a complex sort of proposition.
Arnauld’s approach to the theory of the syllogism is primarily meta-logical.
Language and Logic in the Post-Medieval period, E J Ashworth 1974 https://www.amazon.com/Language-Post-Medieval-Synthese-Historical-Library/dp/9027704643
Arnauld is said to be the first to use the various principles involved systematically as an axiomatic basis for the theory of the syllogism.
Arnauld after defining “syllogism” and before considering the various moods and figures of categorical syllogisms, formulates a number of axioms and rules which must be satisfied by propositions and syllogisms, statements that are about the objects of the logical system, not that are of or within the system itself.
Besides discussing syllogisms containing only simple propositions, Arnauld also discusses complex and conjunctive syllogisms.
Complex syllogism has a complex proposition for a conclusion and yet does not have the entire complex subject or complex predicate present in the premise where it should occur, the remainder occurring in the other premise. A conjunctive syllogism is one containing a compound proposition and in which the major premise somehow contains the whole of the conclusion. This type includes conditional and disjunctive syllogisms.
In discussing complex syllogisms, Arnauld formulates a general principle by which one can tell whether an argument is valid without reducing it to one of the standard forms of the categorical syllogisms. According to him, one of the premise must implicitly contain the conclusion and the other one must show that it does, in fact, contain it.
Baynes in An Essay on the New Analytic of Logical Forms (1850), calls it an important simplification of syllogistic law and singles out this principle as a key feature of the Port-Royal logic.
Arnauld presents this meta-logical containment principle as the formula summarizing syllogistic reasoning instead of the Aristotelian dictum de omni et nullo.
In speaking of the technical terms such as Barbara and Celarent, Arnauld merely notes that they are helpful for denoting and remembering the various moods of the syllogism because of the vowels they contain. He fails to mention that the consonants in these terms contain clues for their reduction to a first figure mood.
Fourth and last section of Port-Royal logic was given over to a treatise on “method”. Method arises out of the mental operations of “disposing” or suitably organizing the ideas, judgements, and arguments of a given subject matter so that knowledge will be best obtained or communicated. The method of analysis or “resolution” is discussed here as the appropriate method for discovering the truth. The section and the book then ends with a discussion of the type of evidence relevant for religious and other knowledge based upon human or divine testimony.
There are marked difference in Arnauld’s treatment vs. Descartes’. Arnauld does not oppose the method of analysis to Aristotle’s logic. Secondly, Arnauld does not place quite the same degree of stress on discovery or analysis that Descartes had. Arnauld seems rather to emphasize its counterpart in the Cartesian system, the method of synthesis or “composition”.
For Descartes, the analytic method nearly superseded the synthetic, deductive approach, in mathematics if not elsewhere.
The Port-Royal logic is not so much a textbook in ordinary logic as it is a compendium of logic with negative commentary.
Though Arnauld treats most of the basic topics of deductive logic, he forewarns the reader several times that certain technical details usually deemed absolutely essential to syllogistic logic are of no practical use in learning how to reason well and can therefore be omitted.
Arnauld seems to accept that all correct reasoning can be brought into valid syllogistic form, but he notes that this is ordinarily unnecessary and often amounts to pedantry.
The forms of the syllogism are also seen to be of little value in passing judgement on an argument’s validity. A complex argument might be analyzed into so many syllogisms and thus tested for validity, but Arnauld suggests that “we ought rather to examine the solidity of a reasoning by the light of nature than by mere forms”.
Most sophisms arise not through a deceptive form of argument, Arnauld says, but from some other cause, such as the equivocal use of middle terms.
In spite of Arnauld’s critical attitude, which seems to derive from Descartes, he must be seen as a reformer of logic and not as a revolutionary. He does not dismiss Aristotelian logic or raise a rival system of reasoning to replace it. Syllogistic reasoning per se is not challenged, and Arnauld retains a deductive approach to science or knowledge.
Arnauld kept a lot of topics which he felt offered little or no material aid to the art of logic well into later editions in the face of criticism for having included them. He also goes so far as to defend the usefulness of the technical terminology for the various syllogistic modes. Also, while he does criticize certain topics as overly subtle or technical, he simply states or prefixes his opposition to them without undue rancor or needless repetition. It is also evidenced that the axiomatic treatment of Arnauld on various forms of the syllogism, which apparently originated with him, reveals more care and concern for these topics than could be expected from someone who thought them unworthy of any attention.
Arnauld holds the principle of containment up as the epitome of demonstrative reasoning.
That one premise contains the conclusion does not preclude the conclusion’s being a piece of genuinely new information. Arnauld requires of the premises that they be better known than the conclusion and that the conclusion not be present in the containing premise expressly but implicitly, so that the other premise must be applied to reveal that the conclusion is in fact contained in it. Under these conditions, which Arnauld believes can be met, new knowledge will be generated by syllogistic reasoning.
His principle of containment may possibly have induced later philosophers of an empiricist persuasion, such as Thomas Reid, Lord Kames, George Campbell, and Dugald Stewart, to conclude that nothing new could be gotten by means of syllogistic reasoning, that the conclusion must always be better known than the premises, and even that the syllogism is nothing more than a petitio principii, but this is quite clearly not Arnauld‘s view.
An Essay on Logic — Robert Blakely (1834)
In its critical role, the Port-Royal logic must have appeared at the time to be only moderately opposed to syllogistic logic. One the other hand, as a text in logic, it must have been seen as condemnatory of much that was prized about the Aristotelian system.
In his 1690 Essay Concerning Human Understanding John Locke launched an attack upon syllogistic reasoning which wielded a very powerful influence on developments in the philosophy of logic during the 18th and early 19th centuries.
Four editions, last one in 1700
The Conduct of Understanding (Published posthumously in 1706)
Treatises on Logic, Philosophy, and Epistemology. A Bibliography of the English Language from the Invention of Printing to the year 1800. R C Alston 1970
Locke’s Essay Concerning Human Understanding was undertaken because he became convinced that true knowledge of things was dependent upon a prior investigation of the knowing process itself. For this reason he does not follow Bacon in analyzing the inductive methodology of natural sciences but instead develops an empirical epistemology or philosophy of mind. Locke’s theory of knowledge shares a basic empirical approach to reality with that of Bacon, but it is closer in some ways to that proposed by Descartes and promoted by Arnauld, for all knowledge, in Locke’s view, is of ideas, not of things directly.
The Essay treats all the basic mental operations and their products as set out in the in the Port-Royal and other logics, though its focus is epistemological rather than strictly logical.
For all his antagonism to the traditional logics of his time, he seems to have adopted their general approach (terms, judgements, reasonings). W H Kenney characterizes this synthetic approach as “mechanistic” since the objects of each level are obtained by combining elements of the preceding level in some way.
Encouraged by Locke’s example, later British logicians were to make an even closer identification of logic and epistemology in treatises which expressly purported to be about logic.
Essay gives disproportionate attention to the first two mental operations and their products: ideas and judgements.
In Port Royal logic, the term judgement is (the result of) the mental operation that evaluates and asserts the connection between any two ideas whatsoever. Locke himself uses the term in a more restricted sense, reserving it for only those cases in which probable propositions arise.
Reasoning is slighted and its syllogistic expression attacked. For Locke as for Arnauld, reasoning is very closely allied with judgement, comprising almost an extended form of judgement, needed in cases where intermediate ideas are required to establish the connection between the two ideas under consideration.
Locke’s perception of the three basic divisions is coloured by his conceptual outlook on the relationship between thought and language. According to Locke, “the business [of Logick], is to consider the Nature of Signs, the Mind makes use of for the understanding of Things, or conveying its Knowledge to others. One can judge and reason about things purely in terms of these ideas, by mentally comparing and arranging them. Language is not a prerequisite for either judgement or reasoning, in Locke’s opinion. In order to record our conclusions for ourselves and others, though, “Signs of our Ideas [that is, Words] are also necessary. Words may facilitate reasoning when complex ideas are involved yet “knowledge consists only in perceiving the habitudes and relations of ideas one to another, which is done without words; the intervention of a sound [a word] helps nothing to it.”
The purpose of language with respect to rational discourse Locke finds to be three-fold:
- To make known one man’s thoughts or ideas to another
- To do it with as much ease and quickness as possible
- Thereby to convey the knowledge of things
Language is either abused, or deficient, when it fails in any of these three.
By these criteria and others syllogism was to be found inadequate as a linguistic vehicle for the reasoning process.
Locke’s work Of the Conduct of the Understanding is predicated on the necessity of a complete system of “logical” rules for correcting the natural corruptibility of the human mind.
In thus playing a restraining role on the understanding, Locke’s system is reminiscent of Bacon’s negative approach to logic. And, like Bacon’s aphorisms, Locke’s rules and injunctions are not formulae for reasoning; they are cautions and maxims which relate to the matter and process of thought rather than to its form, to the proper formation of ideas and the unbiased judgement of their relationships. They give, as it were, general conditions and limitations under which right reasoning and knowledge can flourish, but they do not dictate how one is to reason.
Thoughts Concerning Education (1693)
Learning to reason well, Locke says, come only through exercise. Mathematics, according to Locke, furnishes an excellent arena in which to practice argumentation, because there men can become acquainted with the use of clear and distinct ideas that are adequately defined, with propositions that are precisely stated, and with connected trains of demonstrative reasoning in which results are traced back to accepted first principles. Such valuable habits as the study of mathematics engenders will enable one to deal with any situation that calls for reasoning, even ones where only probable knowledge is attainable.
Locke viewed syllogism as an artificial way of reasoning, adapted more to the attaining of victory in dispute, than the discovery or confirmation of truth in fair enquiries. Disputants, in Locke’s view, are merely interested in defending a position adopted at the outset of a debate, regardless of its truth or merit, and not in learning the truth about matter being considered.
John Locke and the Oxford Training in Logic and Metaphysics — W H Kenney (1959)
Those who desire to uncover the truth must investigate things, not words. To progress in this, it is absolutely crucial to form clear and distinct ideas, to decompose them into simpler ideas wherever possible, and to compare the various ideas with one another, either directly or via intermediate ideas. When two ideas are related simply and immediately by perceiving their connection, the resulting judgement is said to arise from intuition. However, due to the limitations of human intuition, ideas usually need to be compared through the medium of interposing ideas, in which case the judgement tying the two extremes together is said to be gotten by means of demonstration.
Locke accuses the syllogism of being unable to further knowledge, and in a sense this is true. For the syllogism depends, he says, on intermediate ideas and their relationships having already been found, so that whatever new connections are discovered in the process have been made by the time the associated syllogisms are formed. Locke does not, however, on the basis of an analysis of the structure of the syllogism or otherwise, instigate a charge of petitio principii, like his followers in the late 18th and early 19th century did.
The syllogism is useless for the discovery either of true results or of their proofs. And, once the ideas necessary to demonstrate a result have been arranged and compared, putting the proof into syllogistic form only makes the argument less perspicuous. This binds the reasoning process by the cumbersome fetters of the syllogism with its contorted repetition of terms, and so tends to clog and hinder the mind which proceeds from one part to another quicker and clearer without them.
Locke at one time thought that even while syllogisms were of no real value in discovering or composing proofs, they were nevertheless still of value in testing their validity. In his Second Vindication of the Reasonableness of Christianity (1697) Locke goes so far as to describe the syllogism as “the true touchstone of right arguing”.
Archbishop Whately and the Restoration of the Study of Logic – A C Fraser 1864 The Life and Letters of John Locke, with extracts from his journals and common-place books — P K King 1858
Locke compared syllogism to a pair of spectacles which some men may find useful for improving their poor eyesight. To promote reasoning as the standard for right reasoning is just as absurd as claiming that spectacles are needed in order for one to see properly.
Locke naturally did not claim that syllogistic logic could not be used by one who was well versed in it to discriminate between valid and invalid arguments, but he did not find it a guide worth acquiring.
Instead of syllogistic, Locke recommends the “short natural plain order” of “juxtaposition”, in which one lays down “the naked Ideas on which the force of the Argumentation depends, in their due order”.
Locke asserts that direct comparison of ideas forms the true foundation of syllogistic inference, for one must decide which modes are legitimate forms of reasoning by means of “the original way of Knowledge, i.e. by the visible agreement of Ideas”.
In Locke’s system of thought, he denies it any useful role in acquiring, proving, or communicating knowledge. It is even less suitable for argumentation in areas in which only probable knowledge is obtainable.
Locke gives two minor criticisms of a more technical nature:
Concerns about arranging the premises of a syllogism so that the middle term can be more easily recognized as such One of the rules by which certain invalid forms of argumentation may be detected and disallowed states that every argument must contain a general or universal premise. This Locke denies outright.
This is supported by his argument which derives from his conceptualist viewpoint on reasoning. Locke argues that all reasoning is actually about particulars because it relates ideas in men’s minds, “which are truly, every one of them, particular Existences.”
While Bacon still saw a legitimate role for the syllogism to play in convincing others of results and deducing consequences from premises which one was required to accept, Locke questions its usefulness across the entire spectrum of human knowledge. The syllogism is inappropriate for carrying an argument forward from its premises to their consequences.
Locke develops Descartes’ view of reasoning as a sequential comparison of ideas and poses it as an alternative form of deductive reasoning, something he was certainly under no compulsion to do. Logicians of his time and later (Aldrich, for example) agreed with Descartes and Locke regarding the validity of the various syllogistic moods resting upon the notions of agreement and disagreement of ideas or terms, even to the extend of formulating their basic canons in these terms, yet they did not for this reason turn back on the syllogistic mode of reasoning.
Locke does not reject the validity of syllogistic reasoning, but he does contents its viability in formulating how people ordinarily deduce conclusions in science, mathematics, and daily life. It is primarily in this area that Locke’s successors in the 18th and 19th centuries are to enlarge upon his work.
Later criticisms of syllogistic logic are made from out of an expanded concept of what the science of logic comprises. During this time period, due largely to Arnauld’s and Locke’s influence, it becomes difficult if not impossible to distinguish works on “logic” from those on epistemology or philosophy of mind.
There is also an inductive trend in the line of Bacon’s work that culminates in the work of Dugald Stewart and John Stuart Mill.
The logics which were the most popular in Great Britain during the 18th century were those of Henry Aldrich, Isaac Watts, and William Duncan.
The logics of Watts and Duncan follows in the spirit of Arnauld and Locke.
Henry Aldrich (1647 – 1710) was Dean of Christ’s Church, Oxford.
Artis Logicae Compendium (1691)
An abridgment of this compendium was published in 1750 by John Wesley, one of the founders of the Methodists. Another abridged version appeared in early 19th century under the title Artis Logicae Rudimenta
This book seems to be the first one in which all 24 valid moods of the syllogism are recognized.
Ivo Thomas’ contribution “Interregnum” to History of Logic
John Wallis Institutio Logicae, Ad Communes Usus Accomodata (1687)
Edward Copleston and his pupil Richard Whately were highly appreciative of Aldrich’s work.
According to Copleston, Aldrich “judiciously compressed and re-cast [Aristotle’s Logic], with increased perspicuity and no loss of matter”.
Logic is defined as the instrumental art directing the mind in the knowledge of things.
The Compendium treats: Simple terms, including the topics of division and definition Propositions: Categorical, Hypothetical Various logical relations holding among categorical propositions (Opposition, Conversion) Categorical syllogisms Hypothetical syllogisms Material considerations relating to the syllogism such as the nature of axioms or principles The nature of proof or demonstration The various levels of evidence for propositions Method: General (Analytic, Synthetic) and with respect to mathematics (axiomatic).
Aldrich’s approach, like that of Arnauld, is axiomatic.
It differs from Arnauld’s in various respects: One of them being the fundamental principles or “canons” taken as axiomatic.
Aldrich formulates his canons of the syllogism in terms of agreement or disagreement of terms. The most important canons are:
- Two terms which agree with a third term agree with each other
- Two terms, one of which agrees with and the other of which disagrees with a third term, disagree with each other.
Aldrich does not attempt to apply his canons directly to syllogistic forms but derives from them 12 general rules governing the structure of the syllogism.
Aldrich determines by a simple combinatorial argument that four types of categorical propositions: A, E, I, and O can be arranged in 64 ways. Using his rules, 12 out of 64 triples are taken as prime candidates for forming a valid propositions. This is done by the 12 general rules he has given based on the axioms.
These canons go back at least as far as the 15th century.
Among the critics of syllogistic logic, Reid is the first to criticize these canons use as an axiomatic basis for the theory of the syllogism.
Logic versus Murray’s Logic. A Criticism — T K Abbot (1881)
Murray’s logic is said to be similar in treatment to that of Aldrich.
In his deductive treatment of the syllogism and in his exposition of the various moods and their relationships, Aldrich stands almost alone among 18th century British logics.
Watts draws his inspiration from the detractors of Aristotelian logic: Descartes, Arnauld, and Locke.
Logick is the art of using reason well in our enquiries after truth, and the communication of it to others. Its purpose is to teach us the right use of reason, so that we can distinguish Good from Evil, as well as Truth from Falsehood.
By reason Watts does not mean only that faculty of the mind which deduces consequences from premises, but rather comprehends it by “all the intellectual powers of man.” These are the faculties which perform the mental operations of perception, judgement, argumentation, and disposition. They give rise to the mental and lingual results of ideas and terms, judgements and propositions, arguments and syllogisms, and ordered discourse and logical method.
De Morgan called the book English Port-Royal Logic.
Watts like Arnauld degrades the technical matters of logic. Though Port-Royal logic still contained a good deal of technical detail, Watts passes over it summarily.
Watts’ alternative to Aristotelian logic is a collection of practical epistemological rules for guiding one in making correct judgements and in avoiding falsehood.
Watts is unlike Bacon and Locke in that he doesn’t talk about replacing the syllogism with inductive logic or in dismissing syllogistic reasoning.
While he ridicules the various moods of the syllogism as ornamentation, he does not scorn syllogistic reasoning in itself or offer another method in its place.
Watts did not attempt to further discredit Aristotelian logic, but neither did he seek to justify or promote it. Logic no longer had the elevated and important position in Watts’ day that it had a century or so earlier, so Watts could afford to be somewhat beneficent toward it. Yet given Watts’ attitude toward and treatment of the syllogism, the popularity of his work as a college logic text indicates a weakening of the place of Aristotelian logic within Britain’s intellectual community.
William Duncan’s Elements of Logic (1748)
William Duncan, Dictionary of National Biography - J Westby-Gibson (1888) Logic and Rhetoric in England 1500 – 1700, W S Howell (1971)
Duncan’s logic originally appeared anonymously as part of the second volume of Robert Dodsley’s The Preceptor containing a general course of education (1748)
The Elements of Logic is primarily a work in philosophy of logic and epistemology, but it is organized in the by-then standard 4 part form of a treatise on logic. First part deals with ideas and shows the strong influence of Locke, particularly in its view of the source and nature of knowledge. Second part deals with judgements and propositions, in the first place with ones that are intuitively evident, but also with those that may require argumentation to be established. There’s a divergence from Locke in here that Duncan stresses the importance of universal propositions and sees particular propositions as somewhat inferior to them with respect to scientific knowledge. Third section is on reasoning and demonstration. Duncan shares both Locke’s antagonism to general maxims and his elevated opinion about the value of mathematical reasoning as a model for other areas of thought. Here and in the fourth section on method, Duncan shows himself quite close to the Port-Royal logic.
Philosophy in the Scottish Universities — J Veitch (1877)
That field which takes account of the Understanding, examines its Powers and Faculties, and shews the Ways by which it comes to attain its various Notions of Things. … [I]t and simple perceptions, through all their different Combinations, and all those numerous Deductions that result, from variously comparing them with one another.
Duncan feels that by thus learning about the actual structure of our minds we will be better able “to conduct our Thoughts, in order to arrive at Truth, and avoid Error.” Though men are rational beings by virtue of their humanity, their ability to reason can be cultivated and improved through knowledge of how their Understanding works.
Through studying mathematics one learns how to demonstrate truth by means of a consecutive sequence of propositions. Mathematics is a paradigm of exact thinking and should be emulated in other fields of thought, such as natural religion and morality.
Duncan’s stated view of logic largely adopts that of Arnauld, thought there seems to be a difference. Arnauld had given logic both an investigative and a communicative function, but Duncan seems to stress only the first. However, this difference is more apparent than real.
Duncan considers the synthetic method as “the Method of Science”.
Scientific knowledge for Duncan is knowledge about abstract ideas and is obtained by intuition and demonstration. Such knowledge need not be purely ideal or hypothetical. As long as one’s ideas are carefully copied from things, true and certain knowledge of the world can be had.
Natural philosophy arises by “trial and experiment”, “by Analogy, and an Induction of Experiments.”
Though it is generally reliable, it is not certain or based in intuition, and hence does not strictly count as “science” for Duncan.
One cannot expect demonstrative truth in natural philosophy; there one reasons more by analogy and induction. One can, of course, introduce reasoning into natural philosophy, as Newton did, but this still does not lead to absolutely certain truths, only to probable knowledge.
Since reasoning and logic are mainly concerned with “science” and not natural philosophy or physics, it is not surprising that Duncan’s logic says little about the nature of the experimental method. Precisely how one empirically arrives at universal concepts and first principles in natural philosophy is not spelled out.
Duncan’s view of the analytic method is that “it traces Things backward to their Source, and resolves Knowledge into its first and original Principles”.
This method is an invaluable aid in discovering the truth of propositions that are not self-evident, in cases where the relationship between the two ideas is not apparent. By searching out middle terms that will connect these, the method of analysis drives the truth of a proposition back to more fundamental principles, and these in turn to even more basic principles until finally the rock-bottom of self-evident truths is arrived at. One then only has to put together these results in their proper order (the method of synthesis or composition) and so demonstrate or disprove the proposition in question. Since all reasoning requires this finding of middle terms, the analytic method is quite important for logic: it is preparatory to all demonstration of non-trivially consequent scientific truths. Nevertheless there are no specific rules which can be given to regulate this process, for the finding of intermediate ideas is dependent upon the extent and depth of one’s knowledge of the field in which the proposition is found.
Though one can and should distinguish “between the Art of Reasoning, and a Syllogism, which is no more than the Expression of it,” yet this distinction is only between “mental and verbal Reasoning.” Duncan seems not to have accepted Descartes’ and Locke’s idea that correct reasoning might be better formulated in another, non-syllogistic manner.
To prove a judgement true for Duncan is to find one or more intermediate ideas which exhibit the asserted connection between the extreme ideas by means of their own relations with them. When these connections are stated as propositions in a regular form, the reasoning is syllogistic.
Technical details of syllogistic reasoning is omitted altogether from Duncan’s work.
Duncan is similarly reticent to provide a technical discussion of sophisms. Anyone who is familiar with correct reasoning can readily detect sophistic reasoning without a set of rules or criteria.
Introduction to the Literature of Europe in the 15th, 16th, and 17th Centuries — Henry Hallam (1837-9)
Cambridge used a variety of texts. These included Locke’s Essay, Watts’ Logick, and Duncan’s Elements of Logick. Sanderson, Aldrich, and Wallis were the main texts studied by Oxonian undergraduates.
Dissertation on the Progress of Metaphysical, Ethical, and Political Philosophy — D Stewart 1821
Scholarship at both Oxford and Cambridge seems to have been at low ebb during much of the 18th century, and the study of logic was probably no exception.
A compendium of logic called An Introduction to Logicks (1701) had been drawn up by the philosophy faculty of St. Andrews at the end of the 17th century with the intention of establishing it as the official university textbook throughout the country, but whether it ever functioned as such is not clear.
The Scottish Philosophy, biographical, expository, critical, from Hutcheson to Hamilton — J McCosh (1874) A History of the University of Aberdeen 1495 – 1895 J M Bulloch 1895 A History of the University of Glasgow from its Foundations in 1451 to 1909 – J Coutts 1909
By about 1730, if not earlier, Locke was beginning to be read and lectured upon in Scotland.
History of the University of Edinburgh: chiefly compiled from original papers and records, never before published — A Bower 1817
John Stevenson (1693/4 – 1775) Influential teacher of logic and metaphysics at Edinburgh (1730 – 177), taught his students logic from Wynne’s Abridgement of Locke’s Essay
J G Heineccius’ Elementa Philosophiae Rationalis et Moralis (1728)
Its approach to logic drew from both Locke and Descartes
Thomas Reid developed his own system of mental philosophy after Hume’s had been established through his Treatise on Human Nature.
Hume’s work provoked Reid to develop his own “common-sense philosophy” to counteract the prevalent philosophical skepticism of his time.
His treatise on mental philosophy, An Inquiry into the Human Mind, on the Principles of Common Sense (1764), repudiated the Lockean view of knowledge, inherited from Descartes and Arnauld, which held that all human knowledge is of ideas and not directly of things. Reid challenged this dogma because he felt that it was the central assumption underlying the skepticism of both Berkeley and Hume. In opposition to this approach to philosophy, Reid asserted that there are a number of principles of common-sense which cannot be further questioned or doubted, for they themselves provide the bedrock of all demonstration.
When the friend of Thomas Reid, Henry Home, Lord Kames (1696 – 1782) requested him to write an appendix on Aristotelian logic for his sketch on the “Principles and Progress of Reasoning“ in his Sketches of the History of Man (1774), Reid accepted the task and produced the most controversial piece of writing on traditional logic since Locke’s Essay.
Reid like Watts and Duncan, adopts the Port-Royal’s view of logic, using it as a touchstone in assessing Aristotelian logic.
Put negatively, logic is the art of avoiding “obscure and indistinct concepts, false judgement, inconclusive reasoning, and all improprieties in distinctions, definitions, division, or method.” Put positively, logic’s goal is to further “the opposite excellencies;” that is, “to teach men to think, to judge, and to reason, with precision and accuracy.”
Reid is strongly opposed to formal logic that he finds logic “purposely darkened‚ by stating the rules of the syllogism in terms of literal symbols. Logic for Reid is rather the art of right thinking, of searching after the truth: “justness and accuracy of thought are the province of logic.”
Consonant with his stress upon truth and accuracy in place of validity is Reid’s emphasis upon “evidence.” Due in part to his desire to combat skepticism with common-sense, Reid is at pains to stress that there are propositions which are evident in themselves and neither require nor admit of any proof. Arnauld is similarly desirous of defending self-evident truths against “Pyrrhonic” or skeptical philosophy in his age.
First principles are established in natural philosophy, as well as in mental philosophy and logic, by means of induction. Here Reid rejects the Cartesian approach espoused by his predecessors, including his English and Scottish compatriots Watts and Duncan, and sides more with Bacon and Newton.
Reid would extend the Baconian or inductive approach to knowledge that had been so valuable for investigating the realm of matter to the world of mental phenomena as well.
The procedures of the mind, Reid notes, are closely allied with phenomena of language. Unlike Locke, Reid believes that “no man can pursue a train of thought or reasoning without the use of language”, words and thoughts being so closely associated. Since language reflects mental procedures so well, Reid feels that an analysis of its structure will yield information about the constitution of the mind.
Reid sees induction as the key process for investigating the world. As logic is the art associated with this procedure, induction is of central importance to it. In sharp contrast to Descartes and his successors, Reid has nothing at all to say about analysis as a method of investigation. Instead Reid adopts and modifies Bacon’s view on the nature of discovery and the place of induction in logic. Reid has boundless admiration and praise for Bacon on this point and others.
Observation and experiment are most important in scientific inquiry; reasoning by itself is sterile and “would only carry a man round like a horse in a mill, who labors hard but makes no progress.”
Eighteenth-Century British Logic and Rhetoric 1971
In the opinion of W S Howell, this charge is close to the Petition Principii. Howell claims that Lord Kames is the first to make this criticism but says that he undoubtedly derived it from what Reid had said. It is really George Campbell in the opinion of Jongsma who first leveled it as an indictment of the syllogism in general, making it an issue to be reckoned with by traditional logicians.
While Reid believes that the process of deduction proceeds from general statements to particular ones contained in them, he does not accuse syllogistic reasoning of circularity.
There are important differences between Reid’s and Bacon’s views. Bacon had set induction against the syllogism as a competing method of demonstration, as a type of proof which could even establish first principles of knowledge. Reid is not so sanguine about induction’s being able to provide certain knowledge.
The evidence of inductive conclusion is only probable not demonstrative in Reid’s opinion. Yet this is all that can in general be expected, according to Reid, for man cannot penetrate to the essence of reality but can only know things “imperfectly”.
Bacon’s inductive method of reasoning is explicitly noted to be “a more effectual engine” than Aristotle’s logic for the discovery of scientific truths.
One who wishes to become a proficient reasoner in some field of discourse, Reid says, need not study the rules of logic, but must above all practice reasoning. Men are by nature rational creatures; it is practice which brings their powers of reasoning to perfection.
“Good sense, good examples, and assiduous exercise, may bring a man to reason justly and acutely in his own profession, without rules.”
Reid seconds Locke in his view that mathematics provides one with an excellent field in which to “strengthen the reasoning power” and that one can learn more from studying those works in which good reasoning is displayed than from studying logic.
Fallacious arguments had been fairly adequately classified by Aristotle for categorical syllogisms, and this had even been extended somewhat by his successors in order to deal with other types of sophisms.
Besides his critique of the use and value of logic, Reid aims several criticisms at syllogistic logic on more technical matters.
Reid is displeased with the way logic had been deductively organized by Aristotle and his modern followers.
Aristotle, Reid says, had proved the legitimacy of the first figure moods by means of the dictum de omni et nullo and had reduced the other moods to a first figure one by means of conversion and opposition. That the entire superstructure of syllogistic logic is based upon such a trivial principle as the Aristotelian dictum Reid takes as proof that logic itself is of little consequence.
Reid reserves harsher criticism for the approach taken by the more modern logicians, such as Arnauld and Aldrich, who invert Aristotle’s inductive procedure in order, as he says, to give logic a façade of scientific respectability. By beginning with the most general principles and proceeding to the various moods, logicians are seemingly able to economize greatly on Aristotle’s labour, for many moods can be ruled out without ever investigating them individually.
The particular axioms he takes issue with are the canons of Aldrich, which he feels can only be considered to be self-evident or axiomatic on the basis of their analogy to the corresponding mathematical axioms. Once they are stated in a distinctly logical fashion — in terms of “affirming” and “denying” rather than “agreeing” and “disagreeing” — their evidential character vanishes. Though Reid does not come out and say so in so many words, one may safely speculate that he feels the evidence for the general rules lies in the validity of the various figures and moods to which they apply.
Reid notes that there are many propositions which do not fit into Aristotle’s mold. Some of these, such as conditional propositions, had been added to traditional logic since the days of Aristotle, but logic was still incomplete on this score.
A class of examples of this are all those mathematical propositions which are relational in nature, such as “A is greater than B”; — they have three terms, the two related things and the relation itself.
Aristotle’s doctrine of the conversion of propositions Reid also thought to be inadequate, since it was only applicable to categorical propositions. Relational propositions such as “Philip was the father of Alexander” and “A is greater than B” can obviously be converted to the propositions “Alexander was the son of Philip” and “B is less than A”, yet the theory of conversion was unable to treat such cases.
Moreover, there are simple inferences involving equality which Reid says cannot be put into syllogistic form. The argument is one involving transitivity of equality: A = B, B = C, therefore A = C.
Reid holds a pivotal position in the history of British philosophy of logic, both because of his negative attitude toward Aristotelian logic and because of his positive outlook on logic and reasoning. In terms of his own approach there are three main emphases which he contributes to further developments in British logic:
- His stress upon evidence. Due to Reid’s influence the evidential character of various types of propositions is treated by most British logicians up to the time of Whately and beyond as very important to logic.
- Reid’s placement of logic within the philosophy of mind was important for the ongoing development of logic over the next few generations. Reid broadens the context of epistemological concerns considerably. He discusses sensation, perception, memory, and so on in his works on mental philosophy. He deemphasizes the operation of reasoning. Like Locke and others, Reid sees the need for demonstration to be due to human incapacity. Reason is not the sole arbiter of truth, as skeptical philosophers like Hume would have one believe, nor is it more trustworthy than sensory perception. All mental faculties have the same Creator and are similarly reliable and prone to error and misuse.
- Incorporation of induction into logic. By breaking with the Cartesian school of thought and in aligning logic with Bacon’s approach, Reid sets the direction which logic would eventually take in the next century.
McCosh notes that induction was also a major emphasis of Reid’s teacher George Turnbull
Reid is a critical figure for it is through his writings that Bacon’s thought comes to the fore in British philosophy of logic.
Both Edward Copleston and Richard Whately feel compelled to combat Reid’s criticisms as a force to be reckoned with.
Lord Kames calls Aristotle’s logic the enchanted castle of syllogism, where phantoms pass for realities and blames it for holding back scientific progress, even in the modern era.
Mathematics alone, he says, has escaped dominion by the syllogism and is, seemingly for that reason, an exemplary model of sound reasoning.
Kames claims that even Aristotle himself, in his various philosophical works, “argues like a rational being, without once putting in practice any of his own rules.”
Unlike Locke and Reid, Kames has little confidence in the study of mathematics for this purpose, because he had found that many good mathematicians were not able to transfer their expertise in reasoning to other realms of thought.
Kames’ criticisms of Aristotelian logic are obviously predicated upon a modern prejudice regarding logic’s scope and purpose. Logic is to be the instrument for acquiring truthful knowledge about the world, not a branch of philosophy which treats the forms of valid arguments.
Kames observes that all of Aristotle’s syllogistic modes are founded upon the logical axiom known as the Aristotelian dictum, which he formulates as follows: “whatever is true of a number of particulars joined together, holds true of every one separately.”
I think this is a wrong formulation because no number of particular elements joined together can give you the higher class.
Kames holds the deductive procedure of the syllogism as backwards, for it passes from the lesser known general proposition to the better known particular one. Kames to a good degree, accuses the syllogism of being useless for formulating demonstrations, because it proves a statement by means of another which is less certain than the one to be proved, being in fact a generalization of it. The syllogism is thus fallacious as a demonstration; it conforms to “the fallacy of undue assumption”. Kames seems a touch hesitant to make his charge in general and asserts this deficiency is present in “the greater part, if not the whole, of his syllogisms.”
Kames thus fails to say plainly that syllogistic reasoning is universally useless for constructing proofs. Yet if he does not accuse all syllogisms of exhibiting the fallacy of undue assumption, he is very close to doing so.
Kames seems not to have entertained the stronger criticism, though, that the syllogism is always and essentially a petitio principii. This was made by George Campbell.
George Campbell (1719–1796)
Campbell doesn’t mention the name of either Reid or Kames, but credits Locke with being the source of his general attitude toward syllogistic reasoning. The result of Campbell’s reflection is nicely organized into four main groups of observations.
- Nature and direction of syllogistic reasoning is opposed to that of “moral reasoning”; that is, to reasoning which leads only to probable, not certain, knowledge. It is therefore not appropriate to apply it to the domain of empirical investigation, for there one must proceed in a reverse manner, passing by means of analysis or induction from particulars to universals.
- In communicating experimental knowledge to others, the synthetic method is not always the most appropriate, though that is its proper domain. Mathematical reasoning can be put into syllogistic form, but that is “incommodious”, being more indirect, more tedious, and more obscure”.
- Elaborating on the first two, he reaffirms the inutility of syllogistic reasoning for matters of experience, saying that its epistemic direction is entirely wrong. Instead of proceeding “from things known to things unknown, and by things evident to things obscure; its usual progress is, on the contrary, from things less known to things better known, and by things obscure to things evident.” Campbell thus gives succinct and unflinching formulation to the charge Kames had broached — the syllogism is a fallacy of undue assumption.
In demonstrating a result — for instance, one that is a universal affirmative (A) proposition — one must smuggle a more debatable proposition into the premises, namely, a proposition in which the property is affirmed of an even broader class of things. Campbell gives other examples as well, including ones which involve singular propositions and premises having co-extensive subjects.
- He asserts that syllogistic reasoning is nugatory because the conclusion of a syllogism is always contained in or asserted by one of the premises. Induction is, for Campbell, the only route to general truths in this field.
Combining this view with the idea that a syllogism is basically no more than particularizing a premise to obtain a conclusion which it contains, he infers that the syllogism is a petitio principii and thus useless for demonstrating empirical results. Campbell therefore ridicules logicians for being concerned about this type of fallacy while at the same time institutionalizing it in their syllogisms. Syllogistic reasoning is at bottom nothing other than begging the question. It establishes results, Campbell says, by means of premises which are themselves less certain and epistemologically posterior to the conclusion.
It is the nature of the syllogism, Campbell says, to deduce a result which is identical with some anterior judgement. A syllogistic argument conveys no instruction, nor does it forward us in the knowledge of things a single step.
It would seem, however, that this is not true of all deductive reasoning for Campbell. Campbell appears to hold that while syllogistic reasoning obtains nothing new, there are deductive arguments, both demonstrative and probable, “in which the principle deduced is distinct from, however closely related to, the principles from which the deduction is made.” Campbell here seems to recognize that there are arguments which, while the consequence is implied by (or implicit) in the premises, are nevertheless epistemically fruitful. If this is the case, syllogistic reasoning must be an impoverished type of deductive reasoning, one which is epistemically unproductive. Campbell unfortunately gives no examples of productive deductive arguments. He also does not say whether such arguments might be recast in syllogistic form, and, if so, where the problem arises.
Campbell does grant the syllogism one slight concession as he turns to look at where syllogistic reasoning might legitimately be engaged. It is definitely not an art of reasoning but for Campbell: “the proper province of the syllogistic science is rather the adjustment of our language, in expressing ourselves on subjects previously known”. By correctly manipulating terms and propositions according to the rules of the syllogism, one will be forced to use words consistently in all one’s propositions. Syllogistic reasoning will not help solve a disagreement on matters of fact, but it may serve to clarify an issue if the difference is merely verbal, one regarding the precise extension of terms as commonly defined.
Campbell opposes induction to the syllogism, though he does not adhere to Bacon’s notion that induction is a form of demonstration.
The charge that the syllogism begs the question was leveled much earlier by Sextus Empiricus and others [A N Prior 1967] but Campbell seems to have “rediscovered” it on his own.
Traditional Logic, A N Prior
Others may have said that syllogistic reasoning is confined to the realm of words and propositions, that it is irrelevant for scientific discovery, that it only goes around in a circle if it is not anchored to observations and experiment, and that it proves better known propositions from lesser known ones, but Campbell explains why this must be so by saying that syllogistic reasoning begs the very question it is to prove.
Judging from the reactions of later British philosophers and logicians, its effect was strongly felt.
First person to discuss the criticism of Campbell’s charge of circularity seems to be Richard Kirwan in his 1807 Logick.
In 1814 Stewart mentions Campbell’s charge of petitio principii with approval and claims that it is “unanswerable”.
In his series of Bampton lectures, he did an exposition of a new system of logic.
The first and most essential office of sound logic is to locate and classify all the different kinds of principles which can form the bases for the various fields of thought.
Tatham picks upon the very thing that Reid looked forward to in an improved logic. The truth-value or degree of certainty of these types of principles are dependent upon their source or evidence; some will be higher or more certain than others in the scale of truthfulness.
Tatham holds that truth is modified by man’s intellectual faculties much as light is refracted by passing through a prism. Truth is thus separated into various degrees.
Each discipline is to be developed in its own unique way. Different areas of discourse require not only different types of evidence and different principles but even different types of reasoning.
A form of reasoning which is necessary and appropriate in one field may be out of place or unattainable in another one. For example, the self-evident axioms of mathematics lead demonstratively to indubitable consequences, but other fields such as natural philosophy or morality cannot achieve this degree of truth and certainty, either in their fundamental principles or their subsequent results.
Whately later combats the view of Tatham that there are different types of reasoning.
Tatham explicitly opposes Locke in his view on the certainty achievable in mathematics and philosophy. He also opposes Locke on the view of the value and role of axioms in mathematics. He thinks it therefore unreasonable, to expect demonstrative reasoning to be the characteristic mode of reasoning in these fields.
Tatham identifies 3 distinct methods of reasoning: inductive, analogical, and syllogistic. These types of reasoning comprise “the whole business of logic, as an instrumental art”.
Tatham, following Bacon and Reid, places most of his emphasis upon the inductive mode of reasoning. Inductive logic is “the true and proper logic of physical science, not that which was employed by the ancient philosophers”. By observation and experiment, carefully noting differences and similarities among particular things or events, one gradually and painstakingly comes to a general conclusion. This process of inference ultimately gives rise to axioms or first principles that form the basis of physical science. As such, induction is prior to deduction; it provides the starting point from which syllogistic reasoning must proceed. The process of induction also supplies syllogistic reasoning with a fund of middle terms for its inferences. Without induction, therefore, syllogistic reasoning can neither get started nor continue to function.
By analogical reasoning one may conclude that since this particular thing or event resembles those others in certain relevant features, it must also share another characteristic with them. This form of reasoning is even less certain than that of induction, for it depends essentially on how well-founded or extensive the similarity actually is.
Analogical reasoning, Jongsma says, is not a clear concept to him from the account of Tatham and that Jongsma considers it rather as a stage in inductive reasoning in which one extends a singular conclusion to other (representative) instances.
This type of reasoning is found almost exclusively in mathematics. Tatham agrees with Aristotle, in opposition to Reid, that mathematical reasoning is essentially syllogistic. But he sides with Reid in judging that it is almost useless elsewhere, for nowhere else besides in mathematics do long trains of reasoning occur.
Tatham like Bacon and Reid before him, faults Aristotle’s logic for its incompetence as an investigative tool for science. The true founder of the logic of science Tatham identifies as Bacon, for he is the first to correctly analyze and esteem the inductive method. Aristotle briefly touched upon the notion of induction, but his induction was “a very vague and imperfect representation of sound and legitimate induction” and he failed to demonstrate its value in his own work.
Tatham’s new system of logic with its attendant criticism of university logic education found both opposition and support in the British intellectual community.
Tatham received appreciative recognition from his mentor, Thomas Reid. Upon receiving a copy of the first volume from Tatham, Reid wrote to thank him and to express his admiration of Tatham’s system of logic. He also promised Tatham that he would recommend it to George Jardine, the professor of logic at Glasgow. Jardine seems not to share the extreme antagonism against Aristotle and syllogistic logic as Tatham.
Philosophy at Oxford — M Pattison 1876 Philosophy at Cambridge — H Sidgwick 1876 The Democratic Intellect: Scotland and her Universities in the Nineteenth Century — G E Davie 1961
Robert Woodhouse seems to have been fairly familiar with Scottish common sense philosophy. Robert Woodhouse was responsible for introducing Leibnizian notation of calculus to England.
By and large, England did not cultivate the philosophy of the mind. Scotland, was quite the reverse. Philosophy of mind was regularly taught in the Scottish universities as an integral part of a mandatory course in logic.
Got an annual 200 pound pension from George III, King of England for his highly popular essay called Essay on the Nature and Immutability of Truth, in Opposition to Sophistry and Scepticism (1770)
Beattie claims that the rules of the syllogism are extremely useful not so much for strengthening the judgement, as for enabling the disputant quickly to comprehend, and perspicuously to express, in what the force or fallacy of an argument consists. He also calls school logic “one of the most successful and most extraordinary effects of philosophic genius that ever appeared in the world.”
These compliments seem to have been more polite than genuine, however, for Beattie has the usual low opinion of disputation. The practice of disputation, he feels, only makes men willing equally to defend or challenge a thesis without respect for its truthfulness; it does not equip them to investigate the truth and resist falsehood.
As school logic inculcates in men the belief that everything must be disputed or reasoned about, men are led away from accepting the most self-evident principles of common sense.
Errors arise mostly from accepting false principles, not from arguing in an invalid mode.
The grand desideratum in logic, therefore, is a set of criteria by which to distinguish “a sentiment of nature from a prejudice of education, a dictate of common sense from the fallacy of an inveterate opinion”.
In 1790 and 1793, near the close of Beattie’s career as a professor, he wrote up his ideas on moral and intellectual philosophy in a two-volume work. In the second volume, he seems to have progressed beyond mere criticism toward a more positive outlook on what logic ought to be.
Logic, as he sees it, is primarily concerned with “evidence”. There is a communicative role for logic (rhetoric is subsumed under logic in his view), but logic is mainly an “art of judging between truth and falsehood, attending to evidence.”
Beattie like Tatham, partitions types of truth, evidence, and modes of reasoning into various categories.
Different sorts of truth are supported by different sorts of evidence: Were one to endeavor to provide any truth by arguments unsuitable to that sort of truth, one would necessarily fall into error and false reasoning.
Elements of Intellectual Philosophy, or an Analysis of the Human Understanding: tending to ascertain the Principles of a Rational Logic
Scott feels that the existing works in logic are still too bound up with “the metaphysical subtleties of the schoolmen; and have little reference to the present advanced state of Intellectual Philosophy.”
A rational system of logic must instead be based on an analysis of man’s mental faculties and should heed “the various kinds of truth” and “the degree of evidence” associated with each. In addition it should focus on “the process of discovery, adapted to each particular science”. Logic also has the correlative task of teaching men how to avoid error and falsehood in these matters.
Scott’s Elements of Intellectual Philosophy — R Woodhouse (March 1807)
Scott’s work is primarily a work in epistemology and is in large measure derived from the works of Reid and Stewart. Scott disagrees with Stewart in several places, most notably with respect to the meaning of abstract terms, where he takes issue with Stewart’s nominalist outlook, but he, like Stewart, holds that a rational logic must be grounded in a developed theory of knowledge.
Scott defines Aristotle’s dictum, which he considers as the self-evident truth, or principle of reason, as whatever is true of the genus, is true of all the species of that genus.
The boasted instrument of the ancient logic, the syllogism, consists in nothing other than a formal expression of this great truth; the major proposition being an enunciation of some general law, the minor, of some specific case of that law, and the conclusion, the obvious inference, that the assertion contained in the major, may be applied to the particular case expressed by the minor proposition.
Scott accepts the basics of syllogistic logic and emphasizes the importance of deductive reasoning while at the same time stressing the need for induction.
William Barron assimilates the critiques and approaches of Locke, Arnauld (very possibly through Duncan), and Reid in his logical lectures.
According to Barron, man’s understanding elevates him as a rational creature above all others and enables him to gain wisdom and knowledge and so improve his lot in life. The art which teaches man to use his understanding rightly, therefore, deserves careful and continuous cultivation. That art is logic. Logic, as Barron defines it, treats “the progress of the understanding in the investigation of truth”.
The primary goal of logic in helping us to learn how to reason rightly is “to inform us how to introduce clearness and good order among our ideas”. This would seem to be a rather restricted viewpoint on logic, especially for a Scotsman of this time period, but Barron holds to it. The theory of logic, he says, “consists of two parts; the nature of ideas, which are the materials on which we reason, and the nature of the faculties or operations of the mind which are concerned in reasoning.” These operations are conceiving, judging, and reasoning. Barron accordingly divides his discussion into three main parts, dealing with ideas, propositions, and syllogisms.
Propositions, for Barron, express the agreement or disagreement of two compared ideas. Reasoning is the operation of the mind which demonstrates the connection between two ideas by means of one or more intermediate ideas. Barron joins Locke here in asserting that reason is most perspicuously and concisely expressed by juxtaposing the ideas involved in their proper order. Deductive reasoning can be put into a series of syllogisms, but this masks the real reasoning process, which is a comparison of successive ideas, and can only be constructed after that is finished. The main business of reasoning is the finding of middle terms, and this depends upon one’s “natural sagacity” and on one’s familiarity with the subject matter at hand.
Barron does not voice Campbell’s critique of circularity, but he does repeat Kames’ criticisms. Syllogistic reasoning leads to trivial or self-evident consequences because it is based on the Aristotelian dictum: whatever is true or false with respect to a genus will also be so for its various species. Apropos of this Barron remarks that “To arrange things into species and genera, is extremely convenient for the purpose of language, and some of the purposes of philosophy; but to pretend to reason from one to the other, seems to be the quintessence of vanity or folly.” No one reasons this way in reality; it is wholly contrived.
Barron deems syllogism as nugatory and insignificant as an instrument of reasoning and is fit only for wrangling and controversy.
Though Barron draws from Reid, his work stands mostly in the line of Locke and differs from Reid.
Though Barron has a high respect for Bacon, especially with regard to his analysis of the sources of error and falsehood, he does not follow his lead on inductive logic. Bacon is seen to be the founder of the true method of investigating the natural world, with Newton being his greatest exponent and practitioner, yet Barron does not feel compelled to treat the topic of induction in his logic.
Man requires art to reason well. Syllogistic logic is of no use in teaching man to reason correctly, but this does not preclude the “salutary” effect that a true logic would have.
Though their conceptions of logic differ with one another and with the traditional Aristotelian viewpoint, yet all are convinced that a system of “logic” is important for guiding man in his epistemic pursuits. Western rationalism, one may conjecture, whether empiricist or idealist, must elevate logic or a theory of rationality to a position of eminence, for it is reason that is thought to distinguish man from beast and allow him to know and to transcend nature.
Most important philosophical heir of Thomas Reid was Dugald Stewart.
Elements of the Philosophy of the Human Mind Three Volumes First volume in 1792: Various operations of mind Second one in 1814: Reasoning and logic, broadly conceived Third Volume in 1827: Phenomenon of language and several other topics
Stewart’s attraction for contemporary French philosophy conjoined with his own moderate or “meagre nominalism”, as James McCosh later termed it, sets him apart from Reid and gives his system of thought some interesting twists, as we will see.
Stewart’s first volume does not develop a positive system of logic. It rather lays the groundwork for it by discussing the philosophy of mind.
For Stewart the connection between mental philosophy and “logic” is so close that at times they seem to be identical. Stewart develops one of those tendencies so prominent in Reid’s view of logic, namely, the alignment of logic more completely with the philosophy of mind or epistemology.
In the spirit of Reid, Stewart treats more than conception, judgement, and reasoning in his work. The intellectual operations that Stewart treats in the first volume are: perception, attention, conception, abstraction and generalization, association of ideas, memory, and imagination.
Abstraction and generalization, the use of general terms and general propositions, are admitted — even defended — by Stewart as distinguishing man from lower animals and making science possible. The use of a general, abstract term, however, in no way commits one to believe in the existence of a general referent or idea. Stewart adopts Adam Smith’s view that each such common term originates as a name of a particular object and that it is later used to identify other similar objects, until finally it becomes a class name. A proposition containing general terms, therefore, “comprehends” the various specific truths gotten by particularizing these terms. It is thus merely a compact statement whose meaning is its many particularizations.
Establishing general propositions can take place in 2 ways:
- One can demonstrate a general proposition by arguing about a specific instance, taking into consideration only those generic properties common to all such cases. This is the procedure of geometry, where one’s argument is formulated in terms of a particular figure drawn to assist the proof.
- Ignore the class of instances altogether and manipulate the general terms provided by the language. This course is analogous to that taken in algebra.
While Stewart does not see these two procedures as completely different (for the particular case of the first method is used “merely as a sign or representative, and differs from any other sign only in this, that it bears a certain resemblance to the things it denotes”), he does stress the crucial significance of language with respect to reasoning.
Stewart takes exception to Locke’s idea that reasoning is the comparison of ideas and can be accomplished without the use of language. He sides instead with Leibniz and Condillac who hold that “a talent for reasoning must consist, in great measure, in a skillful use of language as an instrument of thought.”
In the first volume of the Elements, Stewart had highly recommended constructing an art of logic (though not the traditional one) for guiding intellectual endeavors. Recognizing that Locke and others could produce examples and arguments against such a position, Stewart nevertheless asserted that such an art, if properly based, could only be to the good. By means of it time and energy are saved. Just as in any other craft, technique makes all the difference between a skilled artisan and a novice.
Abstract reasoning can be perfected only to the extent that language becomes truly philosophical. And language itself will become philosophical only to the extent that its general terms do not evoke any particular images; “in other words, it consists in its approaching, as nearly as possible, in its nature, to the language of Algebra.”
In this way reasoning “may be carried on by worlds alone; or, which comes to the same thing, … reasoning [becomes] perfectly analogous to an algebraical operation.”
Stewart backs off from this position by the second volume, partly because he no longer feels that a philosophical language is a realistic goal, but also because he wants to dissociate himself from the position of extreme nominalists and “visionaries” such as Hobbes, Leibniz, and Condillac, whose ideas he thinks tend to undermine the reality of truth and make reasoning too mechanical an affair.
Stewart’s opinion changes so completely by 1814 that, following Reid, he even criticizes Aristotle for making abstract arguments in logic which use general terms and literal symbols.
In the second volume, Stewart develops a positive approach to “logic”. This comprises a discussion of “evidence”, intuitive, demonstrative, and probable, and a treatment of “experimental or inductive logic”.
In 1810 Stewart continues to look forward to an art or system of logic, though he no longer holds out any hope for the development of a philosophical language. Instead he now anticipates logic being improved and expanded by accumulating and updating reflections on the “general rules and methods” of science and mathematics. In the second volume of the Elements (1814) Stewart’s support for an art of reasoning seems to have diminished even further. Stewart certainly finds the Leibnizian ideal of a mechanical procedure of reasoning to be inappropriate to ordinary discourse, for it presupposes that every term used is well-defined. But this goal, which is that of a philosophical language, seems unattainable. In ordinary reasoning, the mind adjusts and fixes the meaning of the terms as it goes along, according to the general drift of the argument.
Stewart gave the most important British analysis of the inductive method between the time of Bacon and that of Herschel (1830), Whewell (1837 and 1840) and Mill (1843).
A Preliminary Discourse on the Study of Natural Philosophy — John Frederick William Herschel (1830) On the Principles of English University Education — William Whewell (1837) A System of Logic, Ratiocinative and Inductive, being a connected view of the principles of evidence, and the method of scientific investigation — John Stuart Mill (1840)
One thing Stewart objects to is the theoretical basis of syllogistic logic. Stewart quotes with approval a lengthy passage from Reid’s tract on Aristotle’s logic in which he concludes that logic is trivial because all the many forms of the syllogism can be reduced to the dictum de omni et nullo.
Stewart then makes 2 criticisms of the Aristotelian dictum:
- In the spirit of Bacon he notes that since a general axiom can only be assumed true after considering its many instances, “it would be more correct to say, that the whole of this science [of logic] is comprised or implied in [this] axiom … [and] that the structure may, with much more propriety, be considered as the basis of the axiom, than the axiom of the structure.
- Stewart contends that a certain formulation of the Aristotelian dictum (the one given by Lord Monboddo in his work on Ancient Metaphysics, which is phrased in terms of “containment” rather than “predication”) is far from being self-evident as a logical principle and so lacks the mark of a true axiom.
Stewart also follows Reid in criticizing the purpose and nature of making logic a demonstrative theory, though he also has his own theory of demonstration to defend. Stewart claims that deducing syllogistic rules from axioms is done “on the obviously false supposition of its being possible to add to the conclusiveness and authority of demonstrative evidence.”
Syllogistic reasoning is already perfectly certain and compelling, being “perfect and complete in itself,” and need not be demonstrated to be so. Aristotle is therefore out of order “in attempting to fortify one demonstration [that is, the syllogism] by another [that is, the proof of its validity].”
Stewart here deviates appreciably from Reid, though he seems to think he is merely elaborating Reid’s viewpoint. For while Reid had correctly claimed that logicians demonstrate that various syllogistic forms are conclusive but said that this was unnecessary, Stewart says that logicians attempt to add to the conclusive force of the syllogism, which they certainly do not. A syllogistic form is either valid or not. Reducing it to a valid first figure mood shows that it is valid, but it does not make it more valid than it was before the proof.
In Stewart’s words: A process of reasoning which pretends to demonstrate the legitimacy of a conclusion which, of itself, by its own intrinsic evidence, irresistibly commands the assent, must, we may be perfectly assured, be at bottom unsubstantial and illusory, how specious soever it may at first sight appear. Supposing all its inferences to be strictly just, it can only bring us round again to the point from whence we set out.
It is obvious that Aristotle’s symbolical demonstrations might be easily thrown into the form of symbolical syllogisms. The circumstance which induced him to prefer the former mode of statement, was probably that he might avoid the appearance of reasoning in a circle, by employing the syllogistic theory to demonstrate itself. It is curious how it should have escaped him, that, in attempting to shun this fallacy, he had fallen into another exactly of the same description; — that of employing an argument in the common form to demonstrate the legitimacy of syllogisms, after having represented a syllogistic analysis as the only infallible test of the legitimacy of a demonstration.
This criticism, which is immediately directed at logicians’ proving the validity of Barbara by means of the dictum de omni et de nullo which summarizes it, might legitimately be extended to demonstrations of the other first figure moods as well. But Stewart cavalierly dismisses all proofs of validity as if they were of the same character, which they definitely are not.
In proving non-first figure moods one reduces them to first figure moods, and this process uses conversion and contraposition, not the informal equivalent of the mood under investigation as a rule of inference. Reid’s summary remarks on what is involved in proving validity are quite accurate, even though he mistakes its purpose because of his view of syllogistic reasoning. Here, too, in straying from Reid by offering his own additional critique of the process of demonstration, Stewart misrepresents what is actually being done.
Besides criticizing the deductive structure of syllogistic logic, Stewart repeats the criticisms of Reid, Kames, Campbell and others regarding the epistemic direction and the intrinsic circularity of syllogistic reasoning. A syllogism, Stewart holds, merely passes from a general proposition to one of its particularizations and so proceeds in the reverse direction to our knowledge.
Campbell was quite astute, Stewart says, when he “hazarded the epigrammatic, yet unanswerable remark” that the valid forms of the syllogism all suffer from a petitio principii.
Stewart does not expend much time and effort debunking syllogistic logic as an organon for science, for he feels earlier criticisms on this score are well known and have made their remark. Even Aristotle’s modern supporters, he says, concede this point to Bacon and his followers.
Demonstrative reasoning, such as occurs in mathematics (and only in mathematics, according to Stewart), may be converted into syllogistic reasoning, but this in no way makes mathematics more perspicuous or convincing.
Though attempts are known to have been made to formulate Euclid’s argument as series of syllogisms, mathematicians and mathematical educators generally realize the folly of such an exercise. This is said to refer to the work of Christianus Herlinus and Coradus Dayspodius which is mentioned by Leibniz. Moreover, mathematics progresses further by such aids as algebra and the analytic method than by adhering strictly to deductive reasoning or the synthetic method. So, while mathematics is in fact an area where the syllogism may legitimately be employed, there are absolutely no good reasons for doing so.
Outside of mathematics long trains of deductive reasoning are rare. And due to the nature of the syllogism, the only possible place in which it might be of any use is in some field in which general principles are given at the outset and one merely wants to apply them to specific cases. Such an area is that of law. Stewart follows Bacon on this matter, but he immediately goes beyond him. Even in law, he says, the practice of syllogistic reasoning appears to be detrimental, for it tends to make lawyers mere disputants favoring their clients’ interests rather than seekers after the truth. Their faculty of judgement is accordingly stunted, for they argue in a one-sided manner. For obtaining the truth in legal or other affairs of daily life, reasoning, and especially syllogistic reasoning, is of little consequence. The development of a sound, unprejudiced judgement is by far more important.
Stewart thus pretty well agrees with Locke’s and Campbell’s assessment of syllogistic logic: it has no real usefulness at all. Because of its historical position, an educated person should be acquainted with syllogistic logic in a general way, but more than this is a waste of time.
Several proponents of Aristotelian logic had asserted since the publication of volume one of the Elements that Aristotle was not only the father of the syllogism but that he was also the originator of scientific induction. This was first put forward by John Gillies in 1797 in his analysis of Aristotle’s works, but also and independently by Francis Balfour in 1809.
Stewart draws distinction between Aristotelian induction and Baconian induction. Aristotelian induction is nothing more than drawing a conclusion from the exhaustive enumeration of all its possible cases (complete induction). It was thus logically a deductive process, not an inductive one in the sense of Bacon. Bacon’s process of induction does not resort to complete enumeration, nor does it merely generalize from an incomplete list of particulars. It rather attempts to infer general propositions by observing which cases are similar and which ones are not and investigating what common cause(s) might account for these things. It does not lead to a necessary conclusion, as Aristotle’s variety of induction does, but when carefully applied it does lead to true and permanent knowledge of the world, not merely imaginary or hypothetical results. It is said that Stewart here manages to misrepresent both Aristotle’s and Bacon’s view of induction.
The results gotten by induction are universal because they are based on the inductive principle first formulated by Reid; namely, that the laws of nature are constant or uniform. (I learnt recently { Apr 2021 } that this is called uniformitarianism.) Stewart allows a limited, heuristic role for hypotheses, unlike some advocates of the inductive method (such as Reid), but scientific knowledge can only be established by means of induction. Induction also provides a method by which one can lay a sound foundation for the science of mental phenomena. Induction alone provides an antidote to skepticism.
Besides advocating inductive reasoning, Stewart throws his support to analogical reasoning. One need not discard this form of reasoning merely because it can be misused. Analogical reasoning is important and yields results about things which could not otherwise be treated. Its validity rests on the “unity and harmony of design” in the universe. It naturally only produces probable conclusions which must be checked out further, but this is itself a significant function. Whenever possible, analogical reasoning should be substantiated by other forms of reasoning or by direct investigation.
Stewart expresses hope that he will construct a rational and practical system of Logic, though he passed away before this could be seen to completion. It remained for John Stuart Mill to build a more elaborate system of inductive logic in 1843 by taking deduction as well as induction into account and linking the two together.
Dugald Stewart — L Stephen (1898)
Before Whately’s response to Stewart’s and other criticism of logic, are taken up, Jongsma backtracks to discuss other defenses of Aristotelian logic which were made in Britain before Whately’s publication. This is so that it will enable to better evaluate how seminal Whately was in the revival of traditional logic in Great Britain.
The discussion will follow defense of Aristotelian logic mounted in Scotland, then the state of syllogistic logic in Ireland, and finally examine some developments and outlooks occurring in England, primarily at Oxford.
Scotland had decidedly turned away from Aristotelian logic during the late 18th and early 19th centuries in favor of mental philosophy and an inductive logic. By the turn of the century, a protest of sorts was taking place against this trend. This was done by two men situated outside the university system, Lord Monboddo and John Gillies, and by one within it, George Jardine of Glasgow University.
Lord Monboddo and some of his contemporaries — W A Knight (1900)
James Burnett (1714 – 1799), later Lord Monboddo was educated at Marischal College, Aberdeen, a few years after his contemporary, Thomas Reid, had been a student there. As a philosophical writer, Monboddo was eccentric and contentious. He early acquired an aversion to Newtonian mechanics which he actively maintained throughout his life in his writings and correspondence. While his contemporaries all around him espoused an inductive philosophy of nature and of mind, Monboddo adopted instead a form of a priori idealism.
Antient Metaphysics: or, the Science of Universals (1779 – 1799)
Monboddo’s defense of Aristotelian logic is of the system as a whole. He feels excused from examining any particulars because the express focus of his work is metaphysics, not logic. He argues that the entire superstructure of the syllogistic logic is based upon the ten metaphysical categories which he distinguished. He claims that Aristotle failed to discuss the source of our ideas, but that this omission is better supplied by a Platonic theory of ideas than by adopting Locke’s viewpoint.
Monboddo claims that every part of Aristotelian logic is indispensably useful for rational endeavors — the distinction between genus and species, the prescriptions for defining and dividing, the doctrines of propositions, and the syllogistic theory of reasoning. With respect to the syllogism, Monboddo asserts that all correct reasoning whatsoever can be resolved into one or more syllogisms.
Monboddo admits that one may reason quite well without a knowledge of logic, but notes that this is no argument against its value. A similar case might be made for Grammar, he says, for many people speak properly without ever having studied the structure of language.
Though the syllogism applies to all types of reasoning and can assume a wide variety of forms, it is nevertheless very simple, being reducible in Monboddo’s view to a principle of containment: if an idea contains or excludes another idea, it must necessarily contain or exclude all the ideas contained within it.
In puzzling over the precise meaning to give to containment, Monboddo notes that in a sense a species both contains and is contained by its genus. His “solution” to this problem is not to distinguish the extension of a term from its comprehension and note that containment can be used in both senses, but to take a species’ containment in a genus to be virtual / potential (because the entire species may not be present at one time) and a genus’ containment in a species to be actual (because all members of the species must actually have the character of that genus).
Monboddo used the syllogism of:
Every Animal is a Substance. Every Man is an Animal. Therefore every Man is a Substance.
People of the time had started to see the notion of “substance” to be empty, must have been highly entertained by Monboddo’s main example.
Monboddo was unable to win his contemporaries over to his position on logic and metaphysics. He was simply too far out of touch with the intellects of his age and had no really compelling line of argument to persuade others that logic was valuable for any real purpose.
Monboddo was submerged too deeply in ancient thought that he refused to entertain the possibility that a modern thinker could have anything better to say on the metaphysics or the philosophy of mind than the ancients. More than that, he failed to meet the criticism leveled by modern philosophers against ancient and medieval philosophy and logic. As far as he was concerned Aristotle had said the last word on logic. All modern treatises could therefore be ignored, either because they needlessly duplicate what Aristotle already said or because they depart from Aristotle and therefore lack real merit.
An issue which had been resurrected and made prominent with Reid’s work of 1774 was the relation between induction and deduction. Monboddo makes no special effort to address this debate, though he does comment on induction. Monboddo describes induction as a process akin to generalization of ideas in which one passes from individual things or particular propositions known “by experience and observation” to a general idea or a universal proposition. This is the method of modern natural philosophy, he says, but it does not lead to certain results or to “science”. Universally true statements can only be obtained by moving in the opposite direction, from a genus to the species or individuals contained under it; they are derived by means of syllogistic reasoning from self-evident axioms. Monboddo is completely at home with such an a prioristic view of knowledge and fails to address the modern criticisms that were aimed at the syllogism with respect to obtaining knowledge of the world; he merely reasserts the superiority of a quasi-Platonic viewpoint.
John Gillies (1747 – 1836)
Aristotle’s Ethics and Politics, Comprising his Practical Philosophy, Translated from the Greek: Illustrated by Introductions and Notes; the Critical History of his Life; and a new Analysis of his Speculative Works (1797)
In the second chapter of the first volume of this work, Gillies presented his “New Analysis of Aristotle’s Speculative Works”, devoting a portion of his discussion to logic. Besides giving an interpretation of Aristotle’s logic, Gillies here defuses some of the arguments which had been urged against it during the preceding century or so. He does this by showing that the main criticisms of Aristotelian logic are misguided and are based upon a misunderstanding of the nature and purpose of logic.
In Gillies’ view, Aristotle’s logic had suffered from two extremes. It had first of all been “shamefully misrepresented” and “grossly misapplied” by medieval philosophers, who “perverted [syllogisms] to purposes for which their inventor declares them totally unfit, and employed [them] on subjects in which his uniform practice shows that he considered them as altogether useless.”
In reacting to this corrupted version of logic, Aristotle’s critics swung to the opposite extreme instead of investigating the subject afresh. They thus “ignorantly depreciated” the art of logic.
In formulating his own interpretation of Aristotle, Gillies rejects the Platonistic version of Aristotle found in the works of Harris and Monboddo. He feels that Aristotle is more accurately portrayed as a “nominalist” than as a realist. Universals are mere constructs, “the work of human thought expressed and embodied in language.”
The basis of Aristotelian logic is not some axiom of containment regarding general ideas, but is instead the key principle underlying the construction of all language; namely, “that things, which have a common nature, receive a common name.”
Things may differ in certain features, but if they share a common characteristic, they may all be called by the term which names that property. Because of this linguistic principle, which might be called “the law of naming,” Gillies claims that the Aristotelian dictum holds true: “Whatever is affirmed or denied of a more general term, may therefore be affirmed or denied of all the more particular terms, as well as of all the individual things to which its signification extends.”
The theory of the syllogism thus rests upon the theory of language-formation. Logic is the art of using language correctly to express both man’s “perceptions of sense” and “the comparisons, abstractions, and conclusions of [his] mind concerning them.”
Under a proper understanding of logic, therefore, one need not flinch at the Baconian criticism that logic deals merely with words, for a knowledge of things depends mainly upon “the proper application of language as an instrument of thought”.
Gillies goes so far as to attribute to Aristotle the view that “the true art of reasoning is nothing but a language accurately defined and skillfully arranged”, a view which he notes “philosophers [Stewart in 1792, among others] have begun very generally to adopt.”
Gillies’ view of the relationship between language and logic makes him a strong advocate of the formal character of syllogistic inference. The conclusion of a syllogism necessarily follows from the premises regardless of what the terms signify; that is, the inference depends solely on the relationship holding among the terms involved. One can therefore substitute letters for words to show the validity of an argument. In fact, “the more abstract and general [the] signs are, they must be the better adapted to show that the inference results from considering them alone, without at all regarding the things which they signify.
The use of letters clarifies the reasoning process by revealing what alone is essential to an argument. Reid therefore showed his ignorance of the nature of reasoning, Gillies says, when he accused Aristotle of making logic dark and mysterious by means of literal symbols.
Gillies’ analysis of Aristotle’s logic provides him with an alternative to the axiomatic approaches to logic.
All modern systems of logic that Gillies analyzed employs the demonstration of the syllogism with 2 axioms:
- Things agreeing with the same third agree with each other
- When one thing agrees with the third and the other does not, they do not agree with each other.
In Gillies’ opinion, Aristotle tells that these axioms do not at all apply to the predication of terms, the one of the other; except when those terms denote mathematical quantities.
Gillies rejects these canons as an improper grounding for logic since they apply only to quantities. The theory of the syllogism is founded instead upon the Aristotelian dictum via reduction to first figure moods and hence, in his view, upon what we have called the law of naming.
Gillies was unperturbed by having logic placed within the realm of words and propositions. He agreed with logic’s critics that Aristotelian logic was not an instrument of scientific discovery, noting that Aristotle never claimed or designed it to be such. Aristotle recognized and promoted the idea that all knowledge originates in sensory experience, arising out of patient observations of the world.
He nowhere opposed induction to definitions or general proposition or syllogistic reasoning but saw them as complementary. By means of generalization from observed particulars, a sure foundation for science is laid in definitions and first principles. Once this is attained, syllogistic reasoning can be used to deduce new results. By properly and accurately defining terms and manipulating true proposition in accordance with the rules of syllogistic logic, progress can be achieved and further discoveries made in the realm of science.
Gillies echoes a sentiment of Stewart’s here, claiming that in many of the sciences, as in mathematics, “our knowledge will be found to advance almost exactly in proportion to the success with which our language is improved.”
The theory of the syllogism also has a preventative part to play in reasoning. Since any correct argument can be written in the form of a syllogism, one can use knowledge of various syllogistic moods to test for validity. In this way, the art of logic enables one to avoid deception and error and embrace the truth.
According to Charles Butler, some people are able to reason well without ever having studied the syllogism, in no way discredits syllogistic reasoning, for “if it be examined why they reason well, it will be found that it is because they reason syllogistically”. Men reason syllogistically when they reason correctly. Aristotle did not invent this form of reasoning, but analyzed it, pointing out the significance of the syllogism for all human discourse.
Aristotle, as Gillies says, knew that human knowledge must be rooted in observation and inductive generalization; it was his scholastic followers in the middle ages who perverted his logic.
A reviewer of Gillies work notes that Gillies thought of logic as being a well-organized language, but that Gillies does point out that Aristotle rejected Plato’s notion of ideas in favor of a nominalistic view of logic.
Gillies claims that induction is the rock bottom of all knowledge in Aristotle’s system.
In the philosophy of Aristotle, induction is the corner stone. He declares explicitly, indeed, that all correct reasoning must proceed from definitions; but whence come definitions themselves? He answers, from induction, that is, in other words, from intellect operating on experience.
Gillies refuses to admit with Stewart that Aristotle’s induction is any different than that of Bacon.
With respect to the critique on epistemic criticism originated by Kames and Campbell, Gillies notes that if this were a valid objection, it would at once destroy all synthetic reasoning whatever; for they all proceed, as syllogisms do, from cause to effect, from generals to particulars.
He dismisses the petitio principii charge as a mere “quibble”. Aristotle already answered this, he says, when he demonstrated that a syllogism, which is “the primary and only complete form of reasoning”, must be composed of “three propositions, distinct and different from each other.” The conclusion is not contained in either premise; a second premise is required in order to deduce the conclusion from the other premise.
Aristotle’s logic is definitely not a tool of scientific investigation, Gillies says, but it is an accurate analysis of the intellectual operations involved in its prosecution. In particular, “the elements of syllogism are essential to all demonstration, for all reasoning whatever, implies a subject about which we reason, premises from which we reason, and a conclusion that is drawn from them. In this sense, then, all valid reasoning is essentially or potentially syllogistic, though it need not be explicitly so in form.”
Scottish surgeon for the East India Company.
Balfour was satisfied when he discovered the strong similarity between his own conclusions and those of Gillies with respect to the relationship of logic and science and Aristotle’s position on induction.
Extracts from the Tehzeeb ul Mantik; or ‘Essence of Logic’, proposed as a small Supplement to Arabic and Persian Grammar; and with a view to elucidate certain Points connected with Oriental Literature (1809)
Logic goes beyond grammar, Balfour says, in being a well-organized language.
The Democratic Intellect: Scotland and her Universities in the Nineteenth Century — G E Davie 1961
Synopsis of Lectures on Logic and Belles Lettres: Read in the University of Glasgow (1797) Ouaedam ex logicae compendiis selecta (1797) Outlines of Philosophical Education, Illustrated by the Method of Teaching the Logic, or First Class of Philosophy, in the University of Glasgow (1818; second, enlarged edition, 1825)
During the initial years of Jardine’s teaching career he had become convinced that the first class in philosophy, which was taught to second-year students, aged 15 or 16, was not suited to the boys’ intellectual maturity. At that time the rudiments of syllogistic logic were taught in conjunction with various doctrines of Aristotelian metaphysics on epistemology and ontology.
Disputation declined at Glasgow, until after 1762 it was no longer practiced at all.
Jardine resolved not to spend the rest of his life teaching a boring course of no relevance to his students’ present state of knowledge or future occupations, and so he gradually modified the curriculum in various ways, both in method of instruction and content.
As Jardine understood it, the primary purpose of the first class in philosophy was not “to expound the doctrines of Logic” nor even “to convey information”, but rather “to stimulate Industry, and cultivate [all] the natural [intellectual] abilities of his Pupils”. Jardine saw his task to be one of teaching students how to think and reason, cultivating not just one or two of their mental faculties but all of them jointly.
Jardine began his lectures with an analysis of all the various mental faculties, distinguishing them from one another and showing their interconnections. Jardine considered the philosophy of mind to be the most appropriate introduction to philosophy as a whole because both moral philosophy and natural philosophy, the remaining components of the philosophy curriculum, were dependent to some extend upon intellectual philosophy.
In the second part of the course Jardine discussed how the different powers of the mind could be strengthened or improved. It was in this portion that Jardine devoted time to logic, both ancient and modern (Baconian). The remaining parts of the course were given over to studying various issues in aesthetics (“the powers of taste”) and to a study of rhetoric, both oral and written.
It is true that Jardine departed even further from teaching Aristotelian logic, but this was primarily due to pedagogical and curricular reasons: he felt that logic was of little value unless it were placed within the context of mental philosophy and that only the essentials could be fathomed by his charges.
In Jardine’s estimation, the way in which logic had been previously taught was not only not of any positive value to the student, it was downright detrimental to his academic development, for it “had a direct tendency to produce habits of negligence, indifference, and inattention; which it is well known, terminate but too frequently in a positive and rooted aversion to study of every description.”
Given these rather strong sentiments, it is somewhat to Jardine’s credit that he retained anything of syllogistic logic at all, however minimal. Whether he did so freely or whether he was compelled to keep a modicum of formal logic in his course, he in any case gave a positive rationale for what he presented.
And given the intellectual climate of the time in Scotland, this was the important thing and is the reason he is considered in the rubric of this essay of defending Aristotelian logic.
Jardine defined logic for his students as the art of conducting the operations of the understanding in the search and discovery of truth.
He distinguished three main stages in the history of logic:
- Pre-Aristotelian stage
- Aristotelian logic
- Modern logic
The first stage of logic, according to Jardine, saw mainly the development of various rules regarding the proper acquisition of ideas, rules about classifying objects, dividing ideas, and defining terms. This part of logic Jardine finds to be most essential to the art of reasoning. One will become a good reasoner if and only if he can obtain correct notions of things.
According to Jardine: If our perceptions be distinct and accurate, our conclusions will seldom be faulty; for, it is obvious, that the more correct our knowledge is of the objects about which we reason, the more just will be our inferences in regard to their properties and relations.
This, he maintains, is the reason why some men can reason well in an area with which they are intimately acquainted and yet reason very poorly in another realm of thought or action. The solution to this problem, therefore, is not to teach men the technical forms of syllogistic reasoning, but to show them how to use “the Logical Instruments of Definition, Division, and Classification”.
Aristotle, Jardine says, extended logic beyond the first part of logic by his exhaustive treatment of judgements and reasoning. The various forms of propositions and syllogisms were invented and studied by Aristotle as a means of analyzing any argument whatsoever with respect to its conclusiveness. As such, this stage of logic marked a big step forward toward attaining “clearness and certainty” in rational discourse; it showed abundant proof of Aristotle’s “great genius and comprehension”.
“The Syllogism”, Jardine says in its defines, “certainly exhibits the best analysis of a simple act [1825 reads “single act”] of reasoning, which consists in the comparison of two things with a third.
It is not an art of scientific or philosophical discovery, but then Aristotle never intended it to be such.
He certainly recognized that the conclusion of a syllogism was implicit in the premises and that it therefore could never contain anything which was, strictly speaking, new or original. This does not make syllogistic reasoning useless, however. It can be legitimately used in developing or communicating results based on axiomatic or indisputable truths, as even Bacon recognized.
The syllogism can be used, Jardine says, to “Ascertain the Accuracy of a Complex Argument” which has already been formulated. By separating an argument into its constituent propositions and testing to see whether the relationships among the ideas involved adhere to the main principle of the syllogism (the Aristotelian dictum), faulty reasoning can be distinguished from sound syllogizing. This function of Aristotelian logic, Jardine claims, is not sufficiently appreciated.
Syllogistic reasoning is rarely used by anyone, in either of the two great divisions of human knowledge, physical science and mental science. Even Aristotle, he observes, seems not to make much use of it outside the Prior and Posterior Analytics. Syllogistic reasoning finds its main application in academic disputation, which may have been taught by Aristotle to his followers, and which was eagerly appropriated by medieval philosophers as an instrument for acquiring and displaying knowledge on a given topic.
Jardine admits that formal disputation has its advantages, teaching the disputant to make clear distinctions, to be precise in his terminology, and to rely only on his own mental prowess, but it has serious drawbacks which more than erase any benefit that might accrue from its use. The habit of disputation makes men itch to argue at length about any issue whatever and without regard for the truth of the matter under dispute.
Aristotle himself, Jardine notes, realized that validity was not a sufficient guarantee of truth, for one could argue in a correct syllogistic mode and still produce falsehood. For this purpose, Aristotle attempted to categorize all the different kinds of fallacies and sophisms, and he discussed the various types of evidence on which arguments could rest. However, Aristotle’s logic remained defective or incomplete on this score, Jardine claims, and it remained for Bacon to inaugurate the third and last stage of logic.
In Jardine’s view, Bacon challenged syllogistic logic’s right to be considered an organon of scientific investigation, and he put forward his own logic of induction to take its place. Bacon naturally did not invent inductive reasoning, but he was the first to systematically advocate and examine its use in acquiring knowledge about the world. Aristotle indeed practiced a sort of induction or inferring from a number of particular instances, but he failed to describe it or insist upon its utter importance in grounding human knowledge.
Jardine admits that an inductive inference does not amount to conclusive proof, but he says that if the induction is properly done, the inference is as convincing as “any demonstration in Euclid.”
Supplementing the logic of induction is Bacon’s treatment of the idols of the understanding, those biases of various types and origins which hinder man from arriving at the truth. Together with the method of induction, these doctrines form the third and final stage of logic.
Inductive reasoning operates in the establishment of first principles in science; syllogistic reasoning is employed in mathematics or any other field of thought in which one may assume a theoretical foundation that has already been laid. Both inductive and syllogistic reasoning, then, have legitimate and distinct roles to play which should not conflict if they are properly executed.
Jardine elevates the inductive stage of logic above the syllogistic because he feels it has accomplished such great things in advancing human knowledge and because he feels that the main part of Aristotelian logic, the rules of the syllogism, are not very important to making men reason well. But he does not pit inductive logic against syllogistic logic or reject the latter.
This partially conciliatory stance toward Aristotelian logic sets Jardine apart from people like Reid, Tatham, and Stewart, and moves him in the direction of such men as Gillies, Copleston, and Whately.
There is one further feature of Jardine’s thought which also separates him from Stewart, that is his estimation of the degree of improvement which logic can bear. Stewart continued to anticipate great changes in logic throughout his entire lifetime, though he changed his mind regarding the nature of the means by which it would be bettered and though he felt his own efforts were no more than a beginning in establishing a more rational or philosophical logic. Jardine thought quite otherwise on this matter. He agreed that “logic” had progressed beyond Bacon, particularly through the efforts of Locke, Reid, Stewart, and others in developing an inductive philosophy of mind, but he did not foresee anything essentially new as forthcoming.
The conviction that motivates and pervades Jardine’s entire work is pedagogical. He believed that for men to learn to reason well, a transformation must occur not in logic itself, but in logic education.
Ireland seems to have maintained a fairly traditional logic program throughout the eighteenth and early nineteenth century in the sole college of its only university, Trinity College, Dublin.
Institutio Logicae. In Usum Juventutis Academicae Dubliniensis (1679) — Narcissus Marsh
The Study of Logic in Trinity College, Dublin — E J J Furlong (1942)
The Provost’s Logic: an unrecorded first issue — M Pollard (1970)
Philip Du Trieu — Manductio ad Logicam
John Locke and the Oxford Training in Logic and Metaphysics — W H Kenney (1960)
Richard Murray (d. 1799) Artis Logicæ Compendium. In Usum Juventutis Collegii Dubliniensis (1759)
Murray rejects Aristotle’s categories, and he makes strong use of the later notions of the comprehension and the extension of terms in explaining and proving various things about propositions and syllogisms, but all things considered, it is fairly Aristotelian.
Logic versus Murray’s Logic. A Criticism. — T K Abbot (1881)
Thomas Kingsmill Abbott (1829 – 1913)
Classical Education in Britain 1500–1900 — M L Clarke (1959)
Murray’s work formed the basis of the logic instruction at Trinity College, Dublin for over a century, until Thomas Kingsmill Abbott managed to dislodge it with his critical pamphlet “Logic versus Murray’s Logic” and with an alternative text, The Elements of Logic (1883).
John Walker (1768–1833)
A Familiar Commentary on the Compendium of Logic used in the University of Dublin (1805)
Walker’s text in logic, ironically enough, found a better reception at Trinity College than Murray’s. In fact, it enabled Murray’s logic to maintain its grip on the university far into the century, for Walker’s Commentary was designated as the official text in the compulsory “pass” course in logic from 1835 on.
Walker feels that a knowledge of logic can be very useful, better equipping a man to reason with his fellows. If a person is familiar with the rules of logic regarding definitions, syllogisms, and so on, he can readily analyze and assess the propriety and validity of another’s arguments. One who has mastered the art of logic thus has a great advantage in detecting and pinpointing inconclusive or fallacious reasoning over one who has never studied it.
Walker’s position on logic’s utility does not lead him to assert that good reasoning requires a strictly syllogistic form. Prescribing such a mode of argumentation, Walker says, would be sheer pedantry. Logic, on the contrary, helps a man know which ordinary kinds of arguments are valid, and it aids him to reject those that are not.
According to Walker, Locke seems not to have had a very deep or accurate understanding of Aristotelian logic, even making some rather elementary blunders in his discussion of it. Locke is quite correct in saying that syllogistic reasoning is not an instrument of scientific discovery, but he is wrong in taking this to be a flaw in Aristotelian logic.
Richard Kirwan (~1733 – 1812)
Logick: or an Essay on the Elements, Principles, and Different Modes of Reasoning
Kirwan seems to have written his treatise in logic because he felt that the standard works in logic were still incomplete, and also because he thought that the reactions of various philosophers to the syllogism were extreme and unfounded and had not been countered as they should have been by writers on logic.
Kirwan thought that a knowledge of logic was essential for all rational discourse, and would not have it be usurped by a one-sided practice in mathematical reasoning, as Locke and his followers advocated.
The study of logic, he says, sharpens the mind for its search after truth. It enables one to resolve controversies and detect falsehood, and it can be used in treating any subject matter whatsoever. Man may be a rational creature, but he continually exhibits his need for methodical assistance in rejecting error. Logic fulfills this role.
Logick is both a science and an art; it is a science in as much as by analyzing the elements, principles, and structure of arguments, it teaches how to discover their truth or detect their fallacies, and point out the sources of such errors. It is an art inasmuch as it teaches how to arrange arguments in such manner that their truth may be most readily perceived, or their falsehood detected.
The proper object of logic, is to determine with precision, the exact significance of words, in what relation soever they may stand, the general and particular properties and varieties of propositions, the nature of ratiocination, the validity of the grounds on which it rests, and lastly, the means of investigating truth.
Logic thus encompasses much more than traditional formal logic. Kirwan does not discuss the various operations of the mind, as his Scottish contemporaries do, but he does incorporate their stress on evidence, something his legal training undoubtedly predisposed him to appreciate.
Reasoning is the deduction or inference of one proposition from two other propositions and is based on the principle “that things that are in any respect the same with, or equal to another, are in the same respects the same with, or equal to each other”.
In alluding to this canon of syllogistic reasoning, Kirwan very nearly restricts reasoning in general to (potentially) syllogistic reasoning. He seems to view the syllogism as the regular or normal expanded form in which all correct reasoning can be placed.
Kirwan alerts his reader to his disapproval of Locke’s stance. He there attributes Locke’s peevishness about the syllogism to his “bile [being] excited by the ridiculous jargon, which in his time, assumed the name of logick”.
Kirwan no doubt felt that his own treatment of the syllogism was exempt from Locke’s censure since it lacked the scholastic subtleties and distinctions. Kirwan merely discusses the syllogism in general terms, giving and illustrating the various principles and general rules underlying all syllogistic forms; he nowhere analyzes or names the various figures or moods in which they can appear.
In defending the utility of the syllogism against Locke, Kirwan notes first of all that syllogistic reasoning differs from ordinary reasoning only in being more completely expressed. Any argument, when made totally explicit, turns out to be a syllogism (or a series of such).
Syllogism is a tool to be used “to express the purport of an argument more distinctly;… to exhibit in a narrow compass the several proposition which, in a long discourse, may have been so dilated, as to escape the memory”
Kirwan notes the negative function of the syllogism as well. Once an argument has been transformed by being put into syllogistic form, it becomes easier “to detect errors in reasoning,” to determine “in what respects the arguments of an adversary are fallacious”. One has a distinct advantage over his opponent if he can point out what rules of reasoning are violated by a fallacious argument. The syllogistic formulation of an argument expedites this matter ad is much to be preferred to Locke’s alternative of merely listing the ideas or terms involved and letting the individual light of each man’s reason determine if the connection be proper or not.
[I]n truth, most mankind reason justly on the common incidents of life, without knowing what a syllogism is, just as they speak without knowing the laws of syntax, and speak prose without knowing what prose is; yet, though they know not the word, they practice what it signifies, when from two propositions they infer a third; and this they must do, whenever they reason, in whatever form or garb of words the propositions may be enveloped.
Kirwan similarly contests Locke’s view that syllogisms are of no value in mathematics. He notes that many mathematicians and logicians, such as Leibniz and Wolff, have held that Euclid’s proofs are very nearly syllogistic in form or are merely a condensed form of a string of syllogisms.
Locke asserts that syllogisms are of no help in discovering new truths about the world. Kirwan agrees, but comes back with an analogy: “Neither do the algebraic rules teach us how to form an equation: are they therefore to be rejected?”
The rules of the syllogism, no more or less than those of algebra, presuppose formulations which state connections between things that have already been discovered. They are then useful for determining the validity of other connections. If a conclusion is already given as the result of an argument, the rules of the syllogism enable one to analyze the justness of the inference. Or, if no argument is stated yet, they give the logician guidance in how to arrange or dispose the argument so as to exhibit the connections. They thus provide a means for discovery a proof of the result, if not the result itself. And where there is some dispute regarding the validity of an inference, the rules of the syllogism are just as necessary to resolving it as the algebraic rules for manipulating and simplifying an equation are to solving it.
The rules of the syllogism are likewise important in establishing probable propositions. They are not just designed for demonstrating certain truths; they are, if anything, more valuable in the realm of probable knowledge. Arguments of a probable nature “borrow their entire convictive force” from their being able to be cast into syllogistic form. The syllogism is the mode of reasoning for testing all argumentation whatever, not just a particular class of arguments.
Kirwan willingly admits that the premises of a syllogism implicitly contain the conclusion; this is, in fact, the nature and the great advantage of the syllogistic mode of reasoning. If someone assumes the premises of a syllogism he is obliged to accept the conclusion as well, for they contain it. An argument is inconclusive only if it violates the principles or rules of the syllogism, which valid moods naturally do not.” Kirwan does not explain exactly how and why this view of the syllogism remains free of Kames’ criticism or Campbell’s charge of circularity.
Gillies’s Translation of Aristotle — Butler (1798) A Familiar Commentary on the Compendium of Logic used by undergraduates in the University of Dublin — Walker (1805)
According to Jongsma, Kirwan was the first person to remark in print on the criticism of circularity from the standpoint of traditional logic.
A review of Kirwan’s work is said to contain the general outlook on the different logics of the time. This period is said to have the growing belief that Aristotelian logic and Baconian logic are not competitors for the same honors but complement one another by performing different functions:
[V]aluable as the Aristotelian logic undoubtedly is, it cannot now of itself be accounted a complete art of reasoning. Its mode of proof by category and syllogism is purely synthetic; and therefore however well contrived for detecting error, it cannot be considered as a fit engine for the discovery of truth, in the various branches of philosophy, both physical and intellectual, which it is now known we can only successfully cultivate by the method of analysis.
The reviewer expresses his hope that a new logic will soon emerge which gives proper due to both the logic of Aristotle and the logic of Bacon, to syllogistic reasoning and to reasoning by induction. Kirwan’s logic he found to be a step in the right direction, though it could not be accepted as the final synthesis of the two logics.
But events were not to progress as the reviewer wished; certainly not at first. The particular way in which Aristotle’s logic was reasserted by some of its proponents brought about a further denunciation of it from the camp favoring inductive logic, as we already saw in our discussion of John Gillies and Dugald Stewart. This in turn pushed the proponents of Aristotelian logic to investigate the merits of induction more closely and to counter the continuing criticism of deductive logic. This trend reached its zenith in the work of Richard Whately, who gave the definitive defense of the syllogism and of traditional logic generally in his day.
18th century England had two “seminaries of higher learning,” Cambridge University and Oxford University. Of these two establishments, Oxford was the more politically and ecclesiastically conservative, “the fortress of the Church of England.”
The Victorian Church. Part I: 1829 – 1859 — O Chadwick 1971 Victorian Oxford — W R Ward 1965 Philosophy at Cambridge — H Sidgwick April 1876 Scholae Academicae: Some Aspects of the Studies at the English Universities in the Eighteenth Century — C Wordsworth 1877 Unreformed Cambridge. A Study of Certain Aspects of the University in the Eighteenth Century — D A Winstanley 1935 Of a Liberal Education in General; and with Particular Reference to the Leading Studies of the University of Cambridge — W Whewell 1845
During the 18th century, the education of syllogism at Oxford has turned out to be farcical and to be more show than substance. Cambridge kept aside the topic of ancient logic in preference for modern natural, mental, and moral philosophy.
At Oxford, toward the end of the 18th century, a number of university officials were beginning to press for reform of the examination system.
People who proposed a new examination statute: John Eveleigh (1747 – 1814) John Parsons (1761 – 1819) Cyril Jackson (1746 – 1819)
Observations, suggested by the Strictures of the Edinburgh Review upon Oxford; and by the two replies, containing some account of the late changes in that University — H H Drummond 1810
Oxford Studies — M Pattison (January 1876)
Henry Kett (1761 – 1825)
Elements of General Knowledge, Introductory to Useful Books in the Principal Branches of Literature and Science. With Lists of the Most Approved Authors; including the Best Editions of the Classics. Designed Chiefly for the Junior Students in the Universities, and the Higher Classes in Schools (1802)
Logic is the art of forming correct ideas, and of deducing right inferences from them; or it may be said to constitute the knowledge of the human mind, inasmuch as it traces the process of all our information, from our first and most simple conceptions of things, to those numerous conclusions, which result from comparing them together.
Kett holds that the ultimate aim of logic instruction is to help men live virtuous lives. Man’s reason can be cultivated and improved through a study of the various mental faculties, and thus man himself can be bettered. By providing the tools for discerning truth, logic helps man to regulate his conduct in a rational and moral manner.
Kett states that Aristotelian logic is inferior to the modern logic of Bacon and Locke.
Logic Made Easy; or, A Short View of the Aristotelian System of Reasoning, and its Application to Literature, Science, and the General Improvement of the Mind: Designed Chiefly for the Students of the University of Oxford.
Kett is said to be not consistent in this treatment. Kett tries to fit a broad conception of logic, such as that held by Duncan and Watts, onto a more limited technical treatise. The result may have passed in the early or middle part of the 18th century (though it would still be flawed by mistakes, but it is quite inconsistent with late 18th and early 19th century developments in logic and mental philosophy.
Edward Copleston (1776 – 1849)
A History of the University of Oxford — C E Mallet 1927
In the course of the criticism from Copleston, Kett’s text was suppressed.
Copleston notes that Bacon had complained that logic was an inadequate tool for the investigation of nature. So it is, Copleston agrees, for syllogizing is “a totally distinct process” from investigating; it ought not to be blamed, therefore, for failing to accomplish what it was never meant to do.
Copleston thus rejects “the confused notion, that Induction has superseded the use of Syllogism, or that they at all enter into competition with each other.”
As a matter of fact, looking at induction as a type of argumentation, it “may be considered as a syllogistic act of the mind, in which the general principle elicited forms the Conclusion.” Copleston accepts a variant of Aldrich’s explanation on this point: “The Minor premiss states that a certain property belongs to a number of individuals, … and the Major premiss … declares that whatever property belongs to these individuals, belongs to the whole class of which they are members.”
As a syllogistic form of deduction, inductive reasoning is completely valid, though the certainty of the conclusion depends on whether the individuals investigated are truly representative of the entire class; that is, on the truth of the inductive premise. If the individual cases comprise the entire class, then the induction is perfect, and the conclusion is actually demonstrated by the reasoning.
The syllogism is not at odds with induction, either as a method of investigation or as a process of reasoning. What’s more, Copleston says, Aristotle was aware of this and correctly related the two.
Aristotle, as well as Bacon, knew that principles are arrived at via induction. Aristotle’s only fault was that he drew his conclusions, particularly in physics, from a knowledge of too few instances. It is quite true, Copleston admits, that Aristotle’s induction is “hasty, scanty, and unsatisfactory” while Bacon’s and his successors’ is “cautious, fully, and convincing.”
Yet, “both Aristotle and Bacon labored in the same cause;” and all things considered, Aristotle’s accomplishments are probably greater than those of Bacon and his heirs. In so discussing the relation of induction to logic, Copleston joins his voice with that of John Gillies. It seems quite likely that Gillies’ remarks on this matter had a formative influence on Copleston.
Copleston advances some points that go beyond Gillies — in very nearly distinguishing between induction as a process of investigation and as a process of reasoning, in asserting following Aldrich, that inductive reasoning can be put into a valid syllogistic form, and in pointing out that the enterprise of modern philosophy is not all that different in epistemic structure from the one which Aristotle pursued in both theory and practice. This point is said to be lying just below the surface and was unearthed and made explicit by Whately.
The proper business of Logic is to make the agreement or the disagreement of two given terms more evident than it was before.
Logic is thus not meant to be an art of reason, in the sense of Watts and Duncan; it is not a tool for acquiring new knowledge. It is more properly taken to be a “an art of Language than an Art of Reason. Its business is to make words subservient to the purpose of communicating our opinions and reasoning to one another.”
Copleston while associating logic very closely with language, does not seem to go as far as Gillies or Balfour, who consider logic to be a well-organized language.
A knowledge of logic enables one to use language to construct sound arguments. In so saying, however, Copleston does not hold that ordinary reasoning must be forced into a strictly syllogistic mode of reasoning.
An argument, then framed according to the strict rules of Logic, would be firm and solid, but if nothing else were added, it would be unfit for use. It is the shell merely, the strong-jointed frame-work.
Armed with the knowledge of all the many valid forms of syllogistic reasoning, a student of logic can be put to work analyzing ordinary arguments “into the syllogistic elements of which they are composed,” for all valid argumentation whatsoever can be resolved into one of these forms.
Aristotle’s logic is the instrument par excellence for disclosing false reasoning and rejecting sophistries. By analyzing a piece of fallacious reasoning into its syllogistic components, one is better able to detect the invalidity of the argument or the falsehood of a premise, which may have been hidden in the ordinary and “irregular” form in which the argument was originally couched.
A real fallacy is such an ingenious mixture of falsehood and truth, so entangled, so intimately blended, that the falsehood is, to use a chemical phrase, held in solution. One drop of sound Logic is that test, which instantly disunites them, makes the foreign substance visible, and precipitates it to the bottom.
Copleston does not make any effusive declarations about the utility of Aristotelian logic or attempt to enlarge its domain to increase its significance, as Kett had, but states its value with respect to rational discourse clearly and concisely, even if not in a connected essay devoted to the topic.
Playfair promoted continental or analytical mathematics over against the geometrical brand of mathematics and mathematical physics still in vogue in Great Britain in 1800s.
In the anonymous review of Laplace’s Traite de la mecanique celeste in Edinburgh Review, Playfair noted that British mathematicians had contributed little or nothing to the development of mathematical astronomy since the time of Newton and Maclaurin.
An important cause underlying this state of affairs was, in his view, the British mathematicians’ preference for the synthetic geometrical approach to natural philosophy over the analytic approach prevalent in Europe. But Playfair sees the real crux of the problem to be institutional in nature.
Playfair criticized the teaching of “dictates of Aristotle” and stated that mathematical science have never flourished in Oxford. He also criticized Cambridge showing his disapproval for the [catechetical] method which was used there.
Memoir of Edward Copleston. D. D., With Selections from his Diary and Correspondence — W J Copleston 1851
Aristotle labored in an age of sophistry and dogmatism to establish the empire of Common Sense and Reason.
His logic was indeed perverted by many into an art of disputatious wrangling and was thus rejected by modern philosophers, Copleston says, but they reneged on their responsibility to look more closely at the merits of the subject afresh and instead accepted the common but erroneous view of logic.
Bacon, Locke, Reid, Kames, and others of like persuasion have all consistently misrepresented logic to their readers and have led many astray with their unjust criticisms of Aristotle and syllogistic reasoning.
Aristotle ought rather to be commended for having so thoroughly analyzed the reasoning process into its elements, reducing them to a system based upon that profound but simple principle, the dictum de omni et nullo.
In his reply to Copleston’s defense, Playfair reiterates his earlier charge that mathematics and science are greatly slighted at Oxford and that the teachings of Aristotle still reign there. He ridicules Copleston’s literalistic interpretation that the decrees of Aristotle referred to must be those of his physics, saying he never dreamed Oxford might be thought that backward. Rather, it is the study of Aristotle’s metaphysics and logic which have hampered the learning of the mathematical and experimental sciences at Oxford.
Only very recently did Oxford examinations incorporate any science or mathematics beyond the barest rudiments; before that, “so far as they were scientific at all, and not confined to the learned languages, [the examinations] turned entirely on the Aristotelian and Scholastic logic;… the new logic, such as it is explained in the Novum Organum of Bacon, was never mentioned.”
In Playfair’s view, Aristotelian logic and metaphysics are at fault for the absence of genuine mathematics and science at Oxford in another sense as well. It is not just that they usurped the place which should have been granted to other, more modern subjects; it is also that Aristotle’s logic is diametrically opposed to the method of modern scientific investigation. Playfair strongly disagrees with Copleston that only Aristotle’s physics could hinder the development of mathematical and experimental science. “The logic of Aristotle is particularly hostile to inductive science. By turning the mind to the syllogistic method, it becomes a very powerful obstruction to that knowledge which is derived, by induction, from experience and observation.”
A more reasoned dialogue on the entire matter probably would have brought to light the different philosophies of education implemented by Oxford and Edinburgh, an issue which Whewell was to clarify later only in the context of Cambridge’s changing educational system.
On the Principles of English Education — W Whewell 1837
Copleston replied to the response made with the central thrust that Aristotelian logic, rightly considered, neither is nor can be in competition with Baconian induction. If Playfair had gone to the trouble of reading the brief compendium in use at Oxford, Copleston says, he would have been spared from making his ill-considered remarks on this matter, for Aldrich specifically comments on scientific induction and its relation to logic, pointing out that Bacon’s organon is not opposed to Aristotle’s.
Reid indeed asserts that they are opposed, but his understanding of Aristotle’s logic is far from sound, and he also misrepresents Bacon on this point.
[I]it is a mistake widely spread, that the Organon of Bacon was designed by the author himself to supersede the Organon of Aristotle. The author himself professes no such design, nor can I discover the slightest intimation of it throughout the whole work.
Bacon’s complaints overall, Copleston says, are about two ancient and medieval practices: “intermixing … the doctrines and rules of logic” with those of physics, and making hasty and unjustified generalization from insufficient data.
Regarding the second concern, Copleston says, Bacon’s accusations is not that his predecessors, and Aristotle in particular, do not make inductions, but that they do not make adequate ones. Thus it cannot be true that Bacon sees the syllogism as playing the same role in Aristotle’s system as his own method of induction does in his.
John Gillies, a faithful interpreter of Aristotle’s philosophy and logic, says Copleston, rightly notes that Aristotle held induction to be the process by which one arrives at first principles and scientific knowledge, not the syllogism.
Regarding the first complaint of Bacon, that logic had contaminated physics research, Copleston observes that “the Logic of Aristotle has no necessary or natural connection” with physics. It therefore is not in conflict with physical investigation. On the other hand, Bacon’s Novum Organum does not yield genuine canons of scientific discovery. Its purpose was rather to combat those attitudes which were blocking the development of an empirical approach to science. Copleston admits that there was real need at the time for Bacon to write his Novum Organum. Erroneous conceptions of induction and scientific investigation needed to be challenged and men needed to be warned of the various “idols” which stood in the way of coming to the truth in interpreting nature.
Yet these matters have been resolved long ago, Copleston says, so Bacon’s work has accomplished what it set out to do and is now primarily of historical interest. Also, the model of scientific investigation that Bacon proposes in the second book of his work is quite primitive and is loaded with far more unmeaning Latin jargon than Aristotelian logic.
Modern scientists successfully engage in physical investigations of all sorts without ever having read Bacon or studied his method of science.
In support of his contention that Bacon does not envision his organon as a substitute for Aristotle’s, Copleston turns to Bacon’s Advancement of Learning, where there are several remarks which countenance a place for Aristotelian logic, particularly in areas where principles must be accepted on authority. These are cited by Copleston as proof that Bacon saw his logic merely as an improvement upon that of Aristotle.
According to Jongsma, Bacon makes statements that reject a peaceful coalition between Aristotelian logic and inductive logic as outlined in the first chapter. Since he strongly opposes inductive reasoning to syllogistic, perhaps more than Reid and Playfair, Copleston is guilty of “trick and juggle” and “party sport” with respect to Bacon.
Because Aristotelian logic “is now confined within its proper limits, and is never suffered to impede the progress of free enquiry”, Copleston sees no difficulty in conjoining the two organons.
[T]here is no incongruity in adopting both according to their several measures of utility: …[to] neglect the one because we are in possession of the other [is] a folly not unlike to that of a man who would discard the windmill, because the steam engine has been invented,…
Copleston thus rejects the analogy which Playfair had formulated regarding the backwardness of an institution which would accept Aristotle’s logic and ignore Bacon’s.
Wallis, Copleston says, who was one of Oxford’s professors of geometry and concerning whom Playfair conceded that “Oxford has an undoubted right to boast as an illustrious mathematician, as one ‘whose writings instructed, and will for ever instruct the scientific world,’ … is famous for having recommended and written a treatise of [Aristotelian] logic, more copious than the Compendium now usually employed.”
Playfair would undoubtedly not have been satisfied with the amount of scientific knowledge required at Oxford nor with the condition under which it was studied, but not being intimately familiar with Oxford’s system and being unwilling to formulate his accusations in a more temperate and precise fashion, he was unable to get the better of Copleston on this matter.
John Davison was a contemporary of Copleston at Oxford. Copleston, according to Davison, has finally set the record straight on this issue. Logic and science are nowhere in competition with one another; induction does not make syllogism superfluous.
Davison wholeheartedly agrees with Copleston’s analysis of Bacon’s position on logic and quotes long extracts from it. Nevertheless, he does qualify a point in the argument. Davison knows that Bacon’s Novum Organum deals with more than physical science, at list in principle, so he backs down slightly from Copleston’s clam in in this regard, saying that while Bacon envisioned the application of the inductive method in the area of mental and moral phenomena, he did not develop his ideas on this topic to any extent. This minor modification does not jeopardize Copleston’s main thesis, however. Syllogistic reasoning and the method of induction are nowhere antagonists of one another. The rift between science and logic, Davison agrees with Copleston, is an artificial one and came about through the writings of such men as Reid, who interpreted Bacon in a biased manner.
Someone who was both more acquainted with Oxford’s system of education and more moderate in his criticisms of logic was Henry Drummond.
Drummond, grand child of Lord Kames wrote that Oxford’s course of studies is about as Copleston asserts, though he takes issue with Copleston’s stance on logic and induction and with his analysis of Bacon on this point. Drummond claims, as Playfair had, that Bacon did indeed oppose his method of induction to the syllogistic mode of reasoning in the realm of scientific discovery. Furthermore, he intended his logic of induction to be employed for more than physical researches.
Drummond describes that:
Now, if any one thing be more certain than another, it is this, that Bacon did intend to substitute the mode of Induction for that of Syllogism, in the discovery of every species of truth; and fortunately for science, his intentions have been well understood by his successors.
Copleston’s interpretation of Bacon, Drummond says, is therefore simply wrong. The Scottish philosophers’ understanding of Bacon is quite correct on these matters. Aristotle’s critics, Reid and Kames, have nicely captured Bacon’s outlook on the syllogism in their denunciation of its evil effects on the growth of science.
Bacon’s contribution to the encyclopedia of knowledge consists, according to Drummond, in promoting “the only mode of useful investigation, from which the attention of his predecessors had been distracted by the prevailing influence of the syllogistic form of reasoning.” Aristotle had no inkling of Bacon’s method of induction. Gillies and Copleston thus falsely attribute this approach to Aristotle. Aristotle naturally used induction, but not in a conscious way. Aristotle “nowhere treats of [induction], or recommends its adoption, and … he was as ignorant of its philosophical application as the unlettered savage is of the law of gravitation”.
In his pamphlet, then, Drummond politely but firmly opposes Copleston, both in his analysis of Bacon and in his view of the place of logic in university education.
In replying to Drummond, Copleston modifies his interpretation of Bacon slightly, and he grants the correctness of Drummond’s account of Oxford examination reforms, but he maintains his perspective on logic and induction unchanged, both in the abstract and in relation to Oxford’s curriculum.
Copleston admits that he may have been a bit overzealous in saying that Bacon’s Novum Organum dealt only with natural philosophy or physical science, but he says that such an outlook is excusable because Bacon does have that principally in view and sometimes speaks as if it is all he has in mind.
But this point was only a subsidiary claim, Copleston says; its refutation does not throw over the main thesis, which was “that the Organon … of Aristotle, if rightly understood, has an object totally different from the Organon of Bacon; and that it is absurd to set up the one against the other, or to regard the latter as a substitute for the former.” The “confusion now so widely prevalent” arises from “the unfortunate use of the same name [organon or logic] for different things”.
In arguing further for this position, Copleston introduces for the first time some passages in which Bacon contrasts his organon with that of Aristotle. In the preceding pamphlet, Copleston had just baldly asserted that Bacon never meant to oppose the two logics. Now he accepts some responsibility for showing that passages which prima facie do oppose them do so only on the surface.
From the passage in Great Instauration, Bacon boasts how superior his “kind of logic” is to Aristotle’s. Bacon notes there that his organon is different from Aristotle’s in several respects, one of them being “the end aimed at,” which in Bacon’s case is “the invention not of arguments but of arts”. Copleston interprets this thrust to mean that Aristotelian logic cannot really be in conflict with Bacon’s, since they serve different purposes.
Copleston also deals with aphorism 127 of the first book of the Novum Organum, in which Bacon says his logic of induction extends to all fields of knowledge, just as syllogistic logic does. This passage, Copleston asserts, demonstrates the very opposite of what it is usually taken to prove. Bacon does not claim his logic to be a substitute for Aristotelian logic, but only a tool whose application gives knowledge in logic, ethics, and politics as well as in natural philosophy.
Copleston thinks that Aristotelian logic may indeed be further improved and that progress may come with the improvement of “the inductive science of mind”, but it makes no sense to discard logic in the meantime.
After looking at these two passages, Copleston reiterates a theme he had brought up in his last pamphlet: Bacon had good cause for denigrating the logical and scientific practices of his day, but no one does any more. Those who ignorantly continue to rail against logic as being unable to produce scientific discoveries totally mistake the true purpose of logic and are like a man who expects a reading-glass to produce words for him even though he has never learned to read. Properly viewed, logic is “the art of effecting conviction, not of acquiring knowledge”. It gives one mastery over what he already knows, enabling him to logically connect various propositions together and so communicate his reasoning to others clearly and coherently. For this purpose, logic deals not with things but with words.
If rightly understood as an art of language, it regulates the universal machinery by means of which the understanding of one man acts upon that of another. As such I have always looked upon it … as the grammar of reasoning by means of words, the humble but necessary foundation on which every solid intellectual fabric must be raised.
Logic thus has an important function to fulfill and should be valued accordingly, even if it is not able to accomplish the nobler task of ascertaining first principles for human knowledge. For this the method of induction must be brought into play, something Aristotle knew full well.
Copleston counters Drummond’s claim that Aristotle did not know or promote a Baconian method of induction by citing several instances in which he discussed this very thing, including 3 passages located within the Organon itself. There, of course, Aristotle was concerned primarily with argumentation and not with methods of investigating nature, Copleston remarks, so what he says of induction is naturally more restricted and differently focussed than what Bacon had to say later.
Jongsma says that here Copleston comes here close to delineating induction as a method of reasoning vs. induction as a method of investigation.
Yet it is obviously the same process which both men discuss. Aristotle’s fault lay not in lacking a theory of induction but in applying it too incautiously.
William Rowe Lyall (1788—1857)
Lyall subjects Stewart’s opinions to close and serious scrutiny. He does this on three main issues, two relating to Stewart’s criticisms of Aristotelian logic and the third dealing with his over-all approach to mental philosophy and to logic in particular.
The first criticism of Aristotelian logic that Lyall takes up is Stewart’s censure of Aristotle for thinking he could demonstrate or strengthen the conclusiveness of a demonstration.
Lyall agrees that such an aim is quite ridiculous and claims that the whole tenor of Aristotle’s Organon is against such a view. Lyall therefore upbraids Stewart for not using his ingenuity to show that this could not have been Aristotle’s intention instead of deriding a position owned by no one.
Lyall’s remarks on this whole matter are not as cogent as they might have been, but he seems to hold that grounding the various moods of the syllogism in the Aristotelian dictum is akin to showing them to be particular cases of the basic forms of reasoning summarized by the dictum — “corroborating the evidence of the particular propositions, by others more general.”
As this is palpably false, Jongsma is hesitant to credit Lyall with the absurdity.
Perhaps Lyall mistook the purport of Stewart’s critique by not being familiar with the process of reduction or by not realizing that that is what Stewart was referring to. At any rate, Lyall shows no recognition of the real purpose of demonstrating the various syllogistic moods from the dictum de omni et nullo, and he fails to point out what is wrong with Stewart’s criticism.
Lyall next treats Stewart’s contention that syllogistic reasoning proceeds in the wrong direction to be of any genuine use in the affairs of human knowledge since it proceeds from universal statements to particular ones and since the conclusion is already implicit in the universal premise. Lyall finds this objection “more plausible” and “better founded” than the other criticism. Yet it is so in appearance only. If the syllogism can be charged with this defect, he says, then so can “all abstract reasoning in general; for syllogism is confessedly nothing but a more expanded form of argument than is usually deemed necessary.”
Lyall does not stop with pointing out the peculiar consequences of Stewart’s view. He does not point out what is wrong with this criticism, but he does attempt to explain why anyone should have found such a criticism of syllogistic reasoning convincing. Unfortunately, his remarks here only succeed in clouding the issue further by introducing irrelevant distinctions and by failing to show how and in what sense a syllogism might lead to new knowledge.
Lyall speaks of a predicate being affirmed or denied of a subject by extension or by comprehension by which means to say it is affirmed or denied in an accidental or essential way. He then claims that if the propositions in a syllogism are of the first type (accidental predication); one does not discover a new truth, but only admits its truth; while if the propositions are of the other type, he believes syllogistic reasoning can be used to discover new truths.
I wonder if there is an example of this in Lyall’s writing.
Notwithstanding this flaw, Lyall does manage to highlight the fact that syllogistic reasoning stands or falls in conjunction with deductive reasoning generally on this matter.
Besides opposing Stewart’s view of Aristotelian logic, Lyall confronts Stewart on his ideal of a rational or inductive logic.
The induction-principle which Stewart put forward as the cornerstone of his inductive logic — that the mind instinctively expects the laws of nature to be constant throughout time — Lyall finds to be rather shaky ground for arriving at truth in science.
More important than his criticism of Stewart’s induction-principle, however, is Lyall’s critique of Stewart’s program of logic and mental philosophy. Stewart, following Reid, was the leading advocate in his day of an inductive approach to philosophy of mind. Lyall challenges the appropriateness of using the inductive methodology of physical sciences for developing these fields.
Since mental objects are not susceptible to experimentation, there is no reason to suppose that they or the mental faculties which produce them can be investigated in the same way as material objects.
Lyall proposes deductive reasoning from general principles (“general reasoning”) as the proper mode of proceeding in mental science, not “inductive analysis.”
Though Lyall defends Aristotelian logic against Stewart’s strictures and rejects the ideal of an inductive logic and philosophy of mind, he does not accept the common outlook that logic is an art of reasoning or disputation. He feels that such a view is in no small measure responsible for logic’s demise in the universities. Because the attendant improvement in one’s reasoning ability is certainly “not commensurate with the time and labour which … [a knowledge of logic] requires”, men wrongly conclude that the study of logic is useless.
Logic is actually the science, not the art, of reasoning.
As the “science of general reasoning,” logic’s “great and leading object is … to exhibit those general laws by which the mind is influenced when it reasons, and to resolve if possible into one common principle the circumstances upon which the conclusiveness of all particular arguments is founded.”
Logic is thus of the greatest theoretical importance for the philosophy of mind and deserves serious study, irrespective of any practical applications.
The principles of logic may indeed have practical application to reasoning, but that ought not to be the rationale for its study. Reasoning may even be learned better by some other means, but the significance of logic would not be thereby diminished. And that some men who have never mastered logic are very good reasoners, is no more an argument against the value of its study than falling bodies are against the study of Newton’s physics.
Aristotle is, of course, not the inventor of the syllogism, any more than Linnaeus is “of shrubs and mosses”, but he is to be admired for “the precision with which he reduces all the conceivable forms of argument into a few distinctly separated divisions”, as well as for various other parts of his treatment of logical theory. Thus, while Lyall would modify the way in which logic is taught and the rationale given for its study, he seems to recommend retaining or reinstating a form of Aristotelian logic in the universities. Logic may have been over-rated in former days, Lyall says, but now it is just as wrongly “under-rated”.
Lyall’s defense of school logic is interesting because:
- It comes from an alumnus of Cambridge. Though Stewart had not really implicated Cambridge with his introductory remarks on syllogistic logic, Lyall recognized that (according to the ordinary way of looking at argumentation) mathematical reasoning and demonstrative reasoning in general were not exempt from his critique. Therefore Cambridge’s mode of education, with its central emphasis on mathematics, was indirectly at stake, too.
- Because of the freshness of his arguments, whatever their shortcomings. Points stressed by Copleston and others are not rehashed by Lyall. And points emphasized by Lyall — the unity of syllogistic reasoning with deductive reasoning generally, the non-inductive character of logic and mental philosophy, and the idea of logic as the science and not the art of reasoning — are either missing or of little consequence in the earlier defenses of Aristotelian logic. Here, too, the focus of Lyall’s academic background may have played a determinative role.
- Lyall’s arguments are interesting in the light of later developments.
Lyall probably had something to do with choosing Whately to write the article on logic for the Encyclopaedia Metropolitana.
Reminiscences. Chiefly of Oriel College and the Oxford Movement — T Mozley 1882
John Hill (1787 – 1855)
Artis Logicae Rudimenta. With Illustrative Observations on each Section (1820)
The Rudiments of the Art of Logic; with Explanatory Notes. To which are Added, Questions for Examinations (1823)
Logic is “an art, not a science.” Its function is “to direct the mind in the knowledge of things.” Logic aids men to better use their mental faculties.
Hill modifies his outlook somewhat by 1828 to put it more in line with Whately’s text, which had been published in the interim. In 1828 Hill says, “Logic is both an art, and a science”, though he then goes on to argue that it is still “more properly called an art,” which is Aldrich’s view of the matter.
Nor does it afford any just objection to the utility of a system of Logic, that many are able to form accurate conceptions, to judge correctly, and to reason well, without having studied any such system; or that many, after a familiar acquaintance with the technicalities of Logic, still continue to be weak reasoners. Without such study the latter may have been still more incompetent: with it, the former could have acquired a still greater command of their reasoning powers.
Hill also deals with another criticism of syllogistic logic, namely, that the syllogism is irrelevant to the acquisition of human knowledge. His remarks on this topic come up in his commentary on inductive reasoning, which Aldrich had placed in the section on “defective” forms of the syllogism. Hill admits here that syllogistic reasoning cannot establish the most basic principles underlying an argument but must accept them from elsewhere.
The ultimate sources of these general principles Hill asserts to be two or three: divine revelation, human intuition, and the “inductive faculty”, the last of which may well also be responsible for those truths deemed to be intuitive. The purpose of syllogistic reasoning is not to discover new truths, but to apply them, however acquired, to obtain less general principles or knowledge regarding a specific situation not before considered. Induction and syllogistic reasoning thus go together, induction preceding the syllogism. In 1828 Hill also credits Aristotle with being the father of the inductive method: “The observation therefore of Aristotle, that induction is prior in its nature to syllogism, appears to be correct.”
The “acknowledged dignity and value of induction” should not, however, lead one “to degrade the syllogistic system.” Just because induction is epistemologically prior to the syllogism does not mean the syllogistic mode of reasoning should be denigrated or the study of logic replaced by the study of the inductive method. For while induction precedes syllogistic reasoning in the affairs of human experience, one must inevitably rely on results and principles based on the testimony of others. Thus one often has more call to use syllogistic reasoning than inductive.
And this necessity [of relying on testimony] appears to be the true reason why the syllogistic system should be the first and most generally understood. For while few have opportunities or power to carry on an inductive process beyond the simple observation of those things which present themselves unsought to their notice, all have daily occasion to use that kind of reasoning which depends on syllogistic principles. No step in common life can be taken without it. It is convenient indeed, if practicable, to obtain an acquaintance with the process by which general principles are acquired; as it is an advantage to the manufacturer to understand the nature and construction of his machinery. Yet if his machinery should be beyond his comprehension, he still finds by experience its utility, and carries on his work. To abolish or to lay aside the use of syllogism, for the sake of devoting every power to the advancement of inductive knowledge, would be not less absurd than if our manufacturers should cease from their beneficial occupations until they should succeed in brining mechanisms to the highest pitch of perfection.
Hill here takes the criticism that logic need not be studied because one can reason without analyzing the structure of the reasoning process and applies it instead to a study of induction — one can profit from the results gotten by means of the inductive method without knowing precisely how they are obtained. And, as syllogistic reasoning is more widely used than inductive, it makes more sense to study logic than the methodology of induction.
Jongsma evaluates that while Hill is part of the revival of logic at Oxford, his work is considerably weaker in respect than it could have been. This is because he does not deal with various issues that had surfaced — epistemic structure and inutility of syllogistic reasoning, induction vs. syllogism, Aristotle and Bacon on syllogism and on induction, the charge of petitio principii, the purpose of axiomatizing logic, and so on.
Hill adhered rather closely to the text of Aldrich in writing his commentary; because of this, his work did not completely fill the void in traditional logic. The definitive synthesis of logic with meta-logic, of a technical treatise in Aristotelian logic with a philosophical defense of its utility, still wanted to be done.
Whately’s logic satisfied the need to have a logic text which informed the reader in a coherent and interesting way of the arguments which had recently advanced in favor of its study and in answer to the criticisms still current at that time. It was much more than a mere synthesis, though. Whately naturally had recourse to arguments which others had fashioned before him, but he tightened them up, formulating them in his own pointed way. He also fortified them with additional arguments and with apt and compelling illustrations, organizing the whole into a more or less consistent and comprehensive theory of logic. For this reason, Whately deservedly emerged as the key figure in the 19th century revival of logic in Britain.
Richard Whately is generally acknowledged by historians of logic as well as by logicians of his own era to be the prime mover in the revival of traditional syllogistic logic in nineteenth century Britain.
It is said that service done by Whately’s is largely ignored or generally slighted for he does not contribute anything directly toward the mathematization of logic.
The Development of John Stuart Mill’s “System of Logic” — Oskar Alfred Kubitz (1932)
O A Kubitz credits Whately with restoring logic to a position of eminence in Great Britain, but more or less in passing, as his main interest is J S Mill’s logic.
Whately’s logic is briefly discussed in B A Brody’s dissertation on the history of the algebra of logic (1967)
The Rise of the Algebra of Logic — Boruch A Brody (1967)
R E McKerrow has given a bit more detail on Whately in his 1974 dissertation
Whately’s Theory of Rhetoric — Raymie Eugene McKerrow (1974)
Whately’s logic is completely ignored by I M Bochenski and W & M Kneale as well as earlier “historians” of logic such as C I Lewis
A History of Formal Logic — Innocentius M Bochenski (1970) Development of Logic — William Calvert and Martha Kneale (1962) A Survey of Symbolic Logic — Clarence Irving Lewis (1918)
Outline of a New system of Logic, with a Critical Examination of Dr. Whately’s ‘Elements of Logic’ — G Bentham (1827) Whately’s Elements of Logic — J S Mill (January 1828) Recent Publications on Logical Science — W Hamilton (April 1833) Logic in The English Cyclopaedia — Augustus De Morgan (1860) Modern Logicians. The Right Hon. and Most Rev. Richard Whately, D.D — S Neil (1862) Arch Bishop Whately and the Restoration of the Study of Logic — A C Fraser (1864)
This thesis by Jongsma is said to be concentrating on Whately’s work primarily as a polemic in defense of syllogistic reasoning and Aristotelian logic and not as a text in logic itself. The technical details of his logic will not be described except insofar as they are required to understand Whately’s contentions about logic or the syllogism. In so doing, however, the key aspects of Whately’s logic will be focussed upon, for, the historical significance of the work lies mainly in its defense of syllogistic reasoning, not in its technical apparatus, which is almost completely taken from Aldrich’s compendium.
Notes fromOriel College Hall — F Trench 1865 Oriel Papers — Cecil Stuart Emden 1948
Whately’s first major publication was his anonymous 1819 work Historic Doubts Relative to Napoleon Buonaparte, which has been characterized as “a witty and attractive reductio ad absurdum of Hume’s short way with miracles.” Written in an age when German rationalistic criticism of the Bible was on the rise, the work was welcomed by orthodox Christians and was republished many times.
Whately is supposed not to have read many others’ work but this does not mean that he was ignorant of what they had to say. Particularly with respect to the criticisms of logic, Whately seems to have been fairly well acquainted with his predecessors’ writings, even if he lacked William Hamilton’s erudition. In some cases his knowledge may have been second hand. His mentor and tutor, Copleston, was supposed to have scoured the literature on logic when he began his career at Oriel, and he no doubt passed on much of what he learned to Whately. Whately seems also to have been familiar with a number of the defenses of logic which had been made prior to his publication.
Whately’s treatise on logic was the result of many years of reflection on the nature of logic and the purpose and value of syllogistic reasoning. Whately notes in the preface to the first edition of his book (1826) that he was “more or less occupied with it” for “about fourteen years” before it was published.
S. T. Coleridge’s Treatise on Method, as Published in the Encyclopaedia Metropolitana — Alice Dorothea Snyder 1932
On April 12, 1822 John Henry Newman was elected fellow of Oriel College. This was much to everyone’s surprise, for Newman had graduated B.A. as a mere pass-man. Newman’s natural shyness, coupled with his awe of Oriel’s fellows and his adherence to various Calvinistic doctrines in theology which they disapproved of made his incorporation into the college problematic. Whately, though he was no longer officially a member of the Oriel community, was still residing at Oxford before taking up his position as rector, and he was enlisted to gently initiate Newman into Oriel life. This he did and with great success, something Newman appreciated for the rest of his life.
Right about his time, according to Newman, “Whately was full of the subject of Logic”, quite possibly because he had been approached to contribute the article on this topic to the Encylopaedia Metropolitana. Newman, who had little appreciation for logic and only a passing knowledge of it prior to his discussions with Whately, was permitted to copy and study Whately’s “Analytical Dialogues on Reasoning”, as they were called.
Whately suggested that Newman transform the dialogues into an essay which he might then use as the basis for his Encyclopaedia Metropolitana article. Newman compiled, working on the “sketch of logic” over the whole month of July and finishing it early in August, just as Whately was preparing to leave for Halesworth. Whately then sent in a slightly revised version of this draft plus some other materials on his article on logic to the Encyclopaedia.
Newman’s essay version of the “Analytical Dialogues” corresponds approximately to the introductory sections (the historical overview and the analytical outline) plus part of the final dissertation on the province of reasoning. Besides finishing these parts of the work, Whately added a synthetical compendium (logic proper), which was based in large measure on Aldrich’s logic, and he composed a chapter on fallacies.
Whately credits Newman as the original author of several pages of the work making a considerable portion of the published work from manuscripts not designed for publication.
Whately may have later denied receiving any material assistance from Newman — it is some such claim that prompted William Monsell to inquire about Newman’s part in composing the Logic in 1852, though he did not tell Newman this at the time — but it is difficult from Monsell’s comments to tell exactly what Whately was denying. Also, by 1852 Newman’s estrangement from Whately was complete, for after having been actively involved in the Oxford Movement, Newman had then gone over to the Roman Catholic Church. Whately was thus no longer very keen on having his name associated with Newman’s.
Newman, in carefully reconstructing his part in writing the Logic years later for his friend William Monsell, seems to suggest that his essay appeared as part of the Encyclopaedia article pretty much as it was written.
Newman’s assertion along these lines is made only with respect to the part of the final dissertation on reasoning which he drew up (based on comparing his copy of it with a proof of the article), and it is said not so much to show that Whately didn’t change what he had written as to prove that he had had something to do with composing that part. Taking this in conjunction with Whately’s above comments, though, it seems possible that Whately treated Newman’s composition — either in total or in part — as we have stated.
Newman himself sometimes writes as if his role in composing the treatise was only to have made a rough draft which Whately then reworked, yet he does not do so consistently. Whatever the case, at least this much is clear — it is Whately, and not Newman, who is responsible for the view of the logic which the article contains.
All this seems to point, then, to more of an editorial role for Newman than anything else. What, then, of Whately’s crediting Newman with being “the original author of several pages”? Whately’s reference here, though he does not explicitly say so, is to the brief survey of the history of logic which appears in the introduction to his work. Two remarks can be made about this. In the first place, the survey seems to be taken from Aldrich, so it is not really Newman’s own production. In the second place, Newman’s part in writing this sketch is not something he was very proud to own later on. In a letter written to Whately late in July, 1822, Newman admitted that he was having difficulties with this part of the treatise. Whether or not he was satisfied with the final result at the time, Whately’s critics were not. In 1833 the redoubtable William Hamilton attacked it in the Edinburgh Review.
Looking back at all this in 1852, Newman confessed that the historical survey was “very shallow and insufficient” and that it “deserved the criticism … it got”.
It would seem, then, that the description Newman gives regarding Whately’s normal mode of operation in constructing a literary work is an apt one for the Logic:
It was a peculiarity of Whately to compose his books by the medium of other brains. This did not detract at all from the originality of what he wrote. Others did but stimulate his intellect into the activity necessary for carrying him through the drudgery of composition.
Newman’s part in composing Whately’s Elements of Logic, therefore, is best described as that of a redactor. This does not minimize the importance of what he actually did, however. Although he did not contribute anything substantial or original to the work and though what he did do may have been further revised by Whately, he did perform a useful function by helping bring Whately’s treatise to completion.
Easy Lessons on Reasoning — Richard Whately (1843)
There are a variety of legitimate and complementary perspectives from which one can view Whately’s Elements of Logic, as his 1826 preface and the work in general make clear. It can be viewed first of all as a work in logic proper. From this perspective, however, there is little original to hold our attention, for as we have already noted, Whately does not go much beyond Aldrich in this respect. The work can also be viewed as a logic textbook aimed primarily at the immediate context of Oxford University. From this perspective the entire work can be accounted for and due weight can be given to Whately’s remarks regarding Oxford examination reforms in logic, for Whately did use his work as a platform from which to criticize the existing system and to urge certain changes.
But a historical approach which focuses on Whately’s logic as a component of Oxford education would soon have to take into consideration the goal of Oxford’s education generally and the role of logic within the curriculum. A classic exposition of this topic is given in E Copleston 1810 Reply. One would thus be led outside the more narrow confines of the educational context to consider the function and purpose of (Whately’s) logic.
Whately explains the value of logic for any human endeavour whatsoever and more particularly in arguing that a knowledge of logic can be a genuine help in defending orthodox Christianity and religious truth against attacks based on falsehood or fallacious arguments. Whately holds this function of logic education to be very important, since he feels that “Among the enemies of the Gospel now, are to be found men not only of learning and of ingenuity, but of cultivated, argumentative powers, not unversed in the principles of Logic.” In order for the defenders of the Christian faith not to be at a distinct intellectual disadvantage and to be able to present “a train of close, accurate, and luminous reasoning” in support of their position, he says, a sound knowledge of logic is required. Whately himself was exemplary in this respect, for he continued throughout his life to defend Christianity as he understood it against a variety of opponents, and he tried to provide the rational trusses for faith in his writings on the evidences of Christianity. Whately’s polemicizing is not restricted to the genre of religious pamphlets; it occurs as well in his logic text, particularly in the appendix which treats ambiguous terms. In fact, his anti-Roman Catholic sentiments were so strongly expressed, that Roman Catholic students were not allowed to study it.
W R Ward observes that Copleston and his pupil Whately survived into the middle of the 19th century, extinct volcanoes in their championing of logic in religion.
To be complete, however, any account of the purported educational value of Whately’s logic would also have to include a discussion of Whately’s defense of syllogistic logic against its detractors. This defense is the core of his logic.
Victorian Oxford — W R Ward (1965) Richard Whately: Religious Controversialist of the 19th Century — R E McKerrow (June 1979)
To be complete, however, any account of the purported educational value of Whately’s logic would also have to include a discussion of Whately’s defense of syllogistic logic against its detractors. This defense is the core of his logic.
Coleridge on Logic and Learning; with selections from the unpublished manuscripts — Alice Dorothea Snyder 1929
Logic, according to Coleridge, is a pure, formal science; that is, it is a science which arises from “pure acts of the Mind” and which considers “the forms under which things in their first elements are necessarily viewed and treated by the Mind.” Its object is specifically “the elementary forms which the Mind necessarily adopts in the processes of reasoning”.
The Science of Logic [consists of] the knowledge of those forms which the conceptions of the Mind assume in the processes of reasoning. And it is manifest that this Science is … subject … to fixed laws; for the reasoning power in Man can operate only within those limits which Almighty Wisdom has thought fit to prescribe. It is a discursive faculty, moving in a given path, and by allotted means. There is no possibility of subverting or altering the elementary rules of Logic; for they are not hypothetical, or contingent, or conventional, but positive and necessary.
None of the defenders of Aristotelian logic who are discussed in this essay speak in this kind of language. Although it might be possible to conceive of this view of logic as somehow arising out of an epistemological or inductivist approach of logic, it would seem more natural for it to have come out of the camp of those taking a formal approach to traditional logic.
This view is taken over from Kant, whose view of logic Coleridge was familiar with, from his Die falsche Spitzfindigkeit der veir syllogistischen Figuren (1762), from his philosophical work, Kritik der reiner Vernunft (1781) and from his manual on logic, Logick, ein Handbuch zu Vorlesungen (1800)
Immanuel Kant in England, 1793 – 1838 — Rene Wellek (1931)
Kant does distinctly side with traditional logic, at least on this point, rejecting the modern trend to expand the boundaries of the field by including epistemological concerns. He remarks in the preface to the second edition of the Critique of Pure Reason that such attempts are predicated on an “ignorance of the peculiar nature of logical science.”
“The sphere of logic”, he goes on to claim, “is quite precisely delimited; its sole concern is to give an exhaustive exposition and a strict proof of the formal rules of all thought, whether it be a priori or empirical, whatever be its origin or its object”. Logic pays no attention to the nature of the evidence underlying an argument, but focuses on the logical connections holding among concepts and among propositions. In the Logic, he circumscribes the field in this way:
Logic is a science of reason not only as to mere form but also as to matter; a science a priori of the necessary laws of thinking, not, however, in respect of particular objects but all objects generatim; it is a science, therefore, of the right use of the understanding and of reason as such, not subjectively, i.e. not according to empirical (psychological) principles of how the understanding thinks, but objectively, i.e. according to a priori principles of how it ought to think.
- Logic is an abstract science
- which studies the necessary laws
- of thought
- namely, the various forms that are determinative of all valid reasoning
Such a view accords quite well with the outlooks of later logicians such as William Thompson and William Hamilton, but does it represent Whately’s position? Our answer to this on the whole must be qualified, “No; at least not in any essential way.”
J B Schneewind’s article on John Stuart Mill
As far as Jongsma knows, there is absolutely no evidence for Whately’s consciously adopting a Kantian viewpoint on logic, though he may possibly have imbibed certain aspects of it from others.
Some of Whately’s stresses do correspond, at least on the surface, to the features we have just identified in Kantian logic, but they may well have come from quite a different source. Moreover, there are other emphases of his logic that definitely do not come from Kant or Coleridge. And conversely, there are certain features of the Kantian viewpoint that are absent in Whately’s account. All things considered, then, Whately’s logic seems not to be directly in line with Kant and Coleridge, though it certainly was not diametrically opposed to the brief prospectus that Coleridge set out for the article on logic in the Encyclopaedia Metropolitana.
The distance which separates a fairly consistent development of this philosophy of logic and Whately’s own can be seen by looking at William Hamilton’s criticism of Whately’s outlook in his 1833 review of the Elements of Logic and by comparing Whately’s view with Hamilton’s brief summary regarding the subject matter of logic which he appended to the article on logic in the Encyclopaedia Britannica a few years later.
Logic, in the most extensive sense which it can with propriety be made to bear, may be considered as the Science and also as the Art of Reasoning. It investigates the principles on which argumentation is conducted, and furnishes rules to secure the mind from error in its deductions. Its most appropriate office, however, is that of instituting an analysis of the process of the mind in Reasoning: and in this point of view it is, as has been stated, strictly a Science: while considered in reference to the practical rules above mentioned, it may be called the Art of Reasoning.
In Whately’s opinion, logic should be considered above all a theory or science of reasoning, though “when applied to practice, it is of course an art or system of rules for right reasoning.” In stressing logic as a science, Whately claims that this aspect of logic has generally been slighted or “expressly denied” and that even Aldrich and his commentator [Hill] argue that it is an art.
Hamilton, in his review of Whately’s logic in 1833, counters this sweeping claim and demonstrates Whately’s ignorance of the history of logic by remarking that “The reverse is true. The great majority of logicians have regarded logic as a science, and expressly denied it to be an art. This is the oldest as well as the most general opinion.”
Historical Sketch of Logic, from the Earliest To the Present Day — R Blakey (1851)
Hamilton then goes on to say that even those who did think that logic was primarily an art did not attribute any real significance to their claim, so Whately’s rediscovery of logic as a science is nothing more than a “useless truism” on which nothing hinges. In limited defense of Whately’s position, however, it should be said that the people he was familiar with and whom we have looked at in the above chapters did by and large treat logic as an art of reasoning. Hamilton’s contemporaries, who were not steeped in the literature of logic to the extent that he was, granted Whately his point, even finding it significant. Furthermore, Whately does make some operational use of his view that logic is a science and not just an art, as we will see, so Hamilton’s criticism is not completely fair.
Though Whately is one of the first in his time and place to stress that logic is a science, we can trace this idea to the logical writings of some of his contemporaries whose works on logic he undoubtedly knew. Whately might have gotten it in the final analysis from Kant or Coleridge, but even if this is so, there is a good chance that it came via an intermediary with whom Whately was better acquainted.
One such candidate is Richard Kirwan, whose definition of logic is given, as William Hamilton observes, “in terms so similar to those of Dr. Whately, that we cannot hesitate in believing that this author had his predecessor’s definition … immediately in view.”
Whately does not counter this criticism in later editions of his Logic and it is quite possible that he read Kirwan and accepted his definition, but Whately’s concept of the subject matter of logic is far more restricted than Kirwan’s. For instance as we noted in chapter 2, Kirwan incorporated a discussion of the nature and types of evidence in his text. Whately, on the other hand, thought that to be quite outside the scope of logic.
Another author whom Whately may have drawn upon is William Lyall, who wrote the 1815 review of Stewart’s volume of logic. Whately does not go along with Lyall in rejecting logic as an art of reasoning, nor does he agree with the Cambridge view that reasoning ought to be taught by means of mathematical study, but he does share Lyall’s view of the subject matter of logic and its educational importance as a theory of general reasoning. Moreover, there are passages in Whately’s logic which seem quite definitely to derive from Lyall’s article.
It thus seems quite possible that Whately’s viewpoint on this matter comes from Lyall, whatever he might have owed Kirwan. Jongsma remarks that he does not know if Lyall was acquainted with Kant’s logic. If this is so, Whately probably fused Lyall’s view with that of Aldrich to get his own. Such a viewpoint would dovetail rather nicely with the axiomatic way in which Aldrich treats logic.
Whately also shares with Kant and Coleridge the view that logic is a formal science. Logic studies the forms of reasoning abstracted both from the meaning of the terms in the propositions and from the truth-value of the premises. In ignoring these things, Whately says, logic is similar to computational arithmetic. Just as one need not know what a set of numbers are numbers of nor whether they are the actual data for a particular situation in order to calculate correctly with them, so also one need not know if the premises of an argument are true or how they were obtained in order to deduce their consequences. One can, Whately says, substitute letters for the terms involved and argue completely in terms of them. Whately notes that this aspect of logic “has been absurdly objected to, even by writers who understood not only Arithmetic but Algebra” [that is, Reid and especially Playfair], but he takes it as “a proof of the strictly scientific character of the system.” Using abstract symbols to examine an argument makes its logical form clearer and thus tends to highlight the nature of the reasoning. As Whately remarks of an argument that is already in syllogistic form,
The advantage of substituting for the terms, in a regular syllogism, arbitrary unmeaning symbols such as letters of the alphabet, is much the same as in Mathematics: the Reasoning itself is then considered, by itself, clearly, and without any risk of our being misled by the truth or falsity of the conclusion, which are, in fact, accidental and variable; the essential point being, as far as the argument is concerned, the connection between the premises and the conclusions.
In voicing this opinion about the formal nature of logic, Whately may have been stimulated by Kant or Coleridge to adopt or stress this point, but I think it is more likely that Whately is merely reasserting a traditional view of Aristotelian logic.
Turning now to consider the subject matter of logic, there seem to be some obvious similarities between Whately’s view and that of Kant and Coleridge, though they are probably no more than that. According to Whately, logic “investigates the principles on which argumentation is conducted”, and it analyzes “the process of the mind in Reasoning.”
For Kant and Coleridge, logic investigates the necessary laws of thought, though rules which the mind must obey in all its reasoning if it is to reason correctly. There is a terminological difference here, for the one uses “laws” while the other uses “principles”, but the two views seem to amount to the same thing, particularly since both go on to speak about these principles or laws as the “rules” of logic.
For Kant and Coleridge, the laws of logic are objective norms, rules which the mind must adhere to in thinking. For Whately, the reasoning process, if it is genuine reasoning, is always the same, no matter what the subject matter — logic studies “that mental process which must invariably take place in all correct reasoning”. All reasoning must obey the rules of the syllogism. In this view, however, Whately need not be indebted to Kant, for it was one that was generally held by traditional logicians, and the syllogistic character of all reasoning had been recently asserted (or very nearly so) by both Kirwan and Lyall.
Both Kant/Coleridge and Whately are likewise concerned to stress that while logic studies mental processes, this should not be done from the viewpoint of psychology or metaphysics, for logic does not study the origin of ideas or the constitution of the mind, but only the process which occurs when one draws correct conclusions from premises.
Whately does not discuss this matter in great detail, but his whole approach is opposed to what we have called the “epistemological“ trend.
Whately, like Kant, is here reasserting the limited scope of traditional logic. His view of the compass of logic seems to derive, however, from earlier texts in logic and not from Kant.
W Hamilton attributes Whately’s view on this matter to the 17th century British logicians Crackanthorp and Wallis, saying that it “has long been rejected”.
In fact, Whately may have restricted the scope of logic even more than his compatriots did who favored the resuscitation of Aristotelian logic, for he writes as if the first two mental operations ordinarily treated by logic texts (conceiving and judging) are only within the purview of logic insofar as they contribute to the reasoning process.
Hamilton terms this “a very partial conception of the science”, as it makes logic “convertible with syllogistic.” Hamilton would have logic treat the formal laws of thought in general, not merely those of reasoning. Insofar as Hamilton is representative of Kantian philosophy of logic in England, we can again see how far Whately is from this viewpoint.
Logic deals almost exclusively, in Whately’s view, with the process of deducing consequences. Terms and propositions are naturally treated in Whately’s logic, but only with an eye to their role in the reasoning process. This makes for a “leaner” logic, more in the tradition of Aldrich; which is not to say that Whately doesn’t include abundant commentary, but that such topics as clear and distinct ideas, evidence, analytic versus synthetic method, and so on are now omitted from the program.
In limiting the subject matter of logic, Whately thought himself to be making a genuine advance for his time. As he saw it, “the greatest mistakes [have] always prevailed respecting the nature of Logic, and its province [has] in consequence been extended by many writers to subjects with which it has no proper connection.” Whately particularly attacks those developments in the 18th century which had diffused the focus of logic. Watts is singled out for censure as the representative of those who had tried to turn logic into a method of directing the mind into the knowledge of all truth. This approach, Whately says, has “a most magnificent object indeed, but one which not only does not fall under the province of Logic, but cannot be accomplished by any one Science or System that can even be conceived to exist.” Logic’s task cannot be to direct the mind in the acquisition of truth. In the first place, logic is not an instrument of discovery or investigation, and in the second place, it does not teach one how to determine the truth of premises and conclusion, but only how to decide whether an argument is valid. In deducing consequences from premises, one need not be concerned about the truth of the premises. Logic is similar to computational arithmetic in this respect — given the data one can calculate with the numbers involved and receive an answer that correctly follows out of the data, regardless of whether the original data is accurate.
Logic is also not to be equated with philosophy of mind. The subject matter of logic is not Reason or all the rational operations of the mind, but reasoning. Whately does not have anything against investigating the various other mental faculties or operations; he may even appreciate some of the developments in this field brought about by the Scottish common-sense philosophers, but whatever their worth, he feels that “it would hardly be possible to build up anything like a regular Science, respecting these matters, such as Logic is, with respect to the theory of Reasoning.” Such rules as might be established in this field might be useful, but “they must always be … comparatively vague and general, and incapable of being built up into a regular demonstrative theory like that of the Syllogism”.
Whately strongly combatted the conclusions of common sense philosophy regarding the worthlessness of logic and syllogistic reasoning, but that did not prevent him from appreciating its outlook on mental philosophy. In 1859 Whately published his own version of mental philosophy in Introductory Lessons on Mind, drawing heavily on Stewart’s views.
Richard Whately on the Nature of Human Knowledge in Relation tot Ideas of his Contemporaries — R E McKerrow (July-September 1981)
Whatever insights mental philosophy has gained may be valid within their own domain, but they should not be incorporated into logic. Such an “extension” of the field of logic, Whately says, would be one in name only, “confounding together … things essentially different”.
While Whately delimits the subject matter of logic as the reasoning process of the mind, he does make some remarks that seem to belie this definition. Following Copleston, Whately thinks of logic, insofar as it is an art, as “the art of employing language properly for the purpose of Reasoning.” This is stated somewhat neutrally, and Whately also says that “Logic is concerned with [language] only when employed for the purpose of Reasoning”.
Whately might be saying no more than many other logicians before him, that language is the instrument of thought, the medium through which logic studies mental operations and objects, though logic’s primary object was nonlinguistic mental phenomena.
But in elaborating the relation between language and logic a few years later, he introduces remarks similar to the above by saying:
In introducing the mention of language previously to the definition of Logic, I have departed from established practice, in order that it may be clearly understood, that Logic is entirely conversant about language.
Whately obviously wants to assert something stronger than that reasoning is generally expressed in words, and after William Hamilton upbraids him in 1833 for his ambiguous and contradictory ideas regarding the precise subject matter of logic, Whately responds that “If any process of reasoning can take place, in the mind, without any employment of language, orally or mental, … such a process does not come within the province of the science here treated of.” It is still possible that Whately is here merely stating with emphasis, in contradistinction to the Lockean view which maintained that reasoning took place in terms of ideas and only incidentally in terms of words and language, that language is essential to reasoning.
An Essay on Logical Method — Charles Peter Chretien (1848) The Life of the Rev. Joseph Blanco White, written by himself, with portions of his correspondence — Joseph Blanco White (1845)
But others at the time and later understood Whately to be taking a nominalistic stand on logic, meaning both that he denied the real existence of universals and that he gave a central role to language in reasoning and logic. Whately goes so far as to call himself a “zealous nominalist.” Whately holds that a common term such as “man” has no referent beyond its individual instances and that it is “merely a name denoting a certain inadequate notion which our minds have formed of an individual, and which, consequently … is applicable equally well to all or any of them”. As all reasoning involves common terms, the necessity of language to reasoning in Whately’s view is evident — language is an essential instrument of reasoning.
Whether this position is inconsistent, as Hamilton asserted, depends on how strictly everything Whately says is to be taken, but centrally, I suppose, on how “reasoning” is defined. Whately makes no claim to having a philosophically tight formulation, but it seems to Jongsma that Whately can legitimately assert that logic both studies reasoning and that it does so strictly in terms of the language in which the propositions and arguments are expressed. His remarks that logic is wholly conversant about language asserts both that logic can only study reasoning which is so clothed, and that no reasoning can occur where language is not used. But regardless of the consistency of Whately’s viewpoint on logic and language, the historical point to be made is that Whately has likely combined the viewpoint of Copleston or Gillies with that of Lyall or of Aldrich or some other, earlier logician, coming up with his own brand of philosophy of logic, one in which language is prominent.
On the utility of Logic many writers have said much in which I cannot coincide, and which has tended to bring the study into unmerited disrepute.
With these words Whately opens his counter-attack on those who would remake logic into something it was never intended to be. Those who mistook logic as “furnishing the sole instrument for the discovery of truth in all subjects, [or] as teaching the use of the intellectual faculties in general … raised expectations which could not be realized, and which naturally led to a re-action”. Though such people thought they were promoting the cause of logic by redefining its purpose and scope, treating it either as the organon of science or as philosophy of mind, they were in fact contributing to its downfall. In consequence of their views, logic properly so-called — the theory of reasoning — “fell … into total disuse.”
Whately’s first task, then, in reviving the study of Aristotelian logic is to explain its genuine utility. This he does at length, both in general terms and in more specific detail.
Logic’s value, as Whately sees it, derives from the ubiquity and significance of reasoning in human affairs. If one were to ponder “what is to be regarded as the most appropriate intellectual occupation of Man”, the answer, Whately says, would have to be, “Evidently in Reasoning.” Though there are many different tasks and vocations, all men are engaged in reasoning: “They are all occupied in deducing, well or ill, Consequences from Premises”.
Logic, considered both as the science and art of reasoning, must therefore be of great importance.
Whately begs his reader temporarily to take for granted that the logical process of deduction embedded in actual argumentation is always and everywhere the same. This being so, he says, it is obvious that the field which systematically studies this rational process and “the principles on which it is conducted” deserves the attention of all liberally educated men. Even if the rules of reasoning had little or no practical application, which he does not believe to be the case, logic would still be entitled to be included in the university’s curriculum, both because it gives “exercise … to the mental faculties” and because it studies “a process which is peculiarly and universally the occupation of man, considered as man”. Logic is thus important as a science, no matter what its worth might be otherwise.
As an art of reasoning, Whately claims, logic has also been wrongly dismissed by its detractors. Faulty arguments have been advanced against logic because these critics have harbored a number of basic misconceptions regarding its purpose and the nature of syllogistic reasoning. One argument which is put forward by various people (Locke and his followers, for instance) states that syllogistic logic is of no value because men have been known to reason well without ever having mastered it. Or, to state a slightly stronger variant of this argument, men do not need a knowledge of logic in order to reason; otherwise men would not have been rational creatures until after Aristotle had devised his system of syllogistic logic.
Whately is said to not always identify his antagonists as is the case here. Whately sometimes tells his reader who has advanced the viewpoints he is countering, but often he leaves them unnamed, preferring to argue against positions and ideas instead of people. In a letter dated to his friend Edward Hawkins, Whately makes the general remark that he has chosen to not use the names chiefly on account of the strong tendency among readers to contemplate everything in the light of a contest between particular writers.
Whately answers these arguments with several retorts. Such arguments can be shown to be absurd, he says, by considering them with respect to other fields of thought. Is the (successful) practice of music or chemistry prior to their systematization an argument against the theory of music or chemistry? Should the fact that people did and do successfully boil water without knowing the modern theory of caloric be counted as an argument against the practical value of the theory of heat? Aristotle did not invent reasoning; he studied it, analyzing and classifying the valid forms which underlie it. He thus has no more claim to having invented reasoning than “Linnaeus to the creation of plants and animals,” or other scientists to the construction or invention of the objective processes or things they discovered.
Jongsma remarks that this viewpoint and illustration is so close to that of Lyall that it is difficult not to attribute it to him.
Criticisms such as these fail to distinguish between the subject matter of logic as a science and the conceptual results which arise out of studying them, and they suppose a peculiar view of what an art or system of practical rules is intended to accomplish.
Logic of course presupposes the existence of correct reasoning; without that no conceptual development of logic as an art (or science, for that matter) would be possible. The problem is, however, that while people are convinced of the value of systematic knowledge in those fields in which they have specialized or are daily employed, they are often content to trust their “common sense” outside of them. Yet it is clear “that Common-Sense is only our second-best guide” whenever recourse can be had to a system of rules “deduced from scientific reasoning aided by experience.” And logic is just such an art or guide for reasoning. Common sense is still required in order to know how to apply the rules of logic to ordinary discourse — this is something that strictly speaking cannot be done by means of the rules of logic, for arguments are generally not given in full syllogistic form. This use of common sense, though, is complementary to a knowledge of logic, and it only reaffirms the importance of the rules being applied.
This point is only added in 1829, quite possibly at the prompting of a passage in J S Mill. In defending Whately’s viewpoint, Mill discussed how a man of common sense might analyze whether or not an argument is valid, and he claimed that the end result (assuming the argument to be valid) must be a series of syllogistic forms. Whately differs from Mill, however, in his view of the process of transforming arguments into syllogistic form, for Mill seems to suggest that this is done according to the rules of logic itself.
As an art of reasoning, logic has both a positive and a negative function perform. Both of these flow out of its teaching one how to distinguish valid arguments from invalid ones. Its contribution on the negative side is that it enables one to recognize and reject fallacious arguments. “Now a fallacy”, Whately says, echoing Copleston, “may aptly be compared to some adulterated compound; it consists of an ingenious mixture of truth and falsehood, so entailed, so intimately blended, that the falsehood is (in the chemical phrase) held in solution: one drop of sound Logic is that test which immediately disunites them, makes the foreign substance visible, and precipitates it to the bottom.”
The charge of Campbell and others, therefore, that logic is an art of wrangling couldn’t be more wrong. Logic should rather be “characterized as ‘the Art of cutting short wrangling,’” because by promoting the analysis of arguments into their elements, the standard forms of syllogistic reasoning, and by providing rules for assessing the validity of an argument, it enables people to determine where their differences lie, if not to resolve the dispute completely. To accuse Aristotle of encouraging contentious disputation with his theory of syllogistic forms, therefore, is ridiculous — “what sophist could ever have consented to restrict himself to one particular kind of arguments, dictated by his opponent?” Though the Greeks may have stressed the value of disputation, even sophistic disputation, they surely meant it, Whately says, as an exercise for sharpening their ability to reason and detect fallacies, as a mental sport and “recreation”, not “as a serious and intrinsically important study”. But regardless of what the Greeks took its place to be within logic, disputation should not be thought of by latter-day students “as [logic’s] principal or proper business”, if indeed “it is to be esteemed as at all falling within the province of Logic”.
Whately seems to be less convinced of the value of disputing in syllogistic forms of reasoning that Copleston was.
Having a number of criteria by which to judge the validity of an argument transforms one into a better reasoner. This positive function of logic is a correlate of the negative function. By making one more knowledgeable about the correct forms of reasoning, one is bound to benefit by being better able to formulate consecutive arguments and repress those that are not. A knowledge of logic enables one “the more readily and clearly to state the grounds of his own conviction … instead of arguing at random without any fixed and acknowledged principles to guide his action.” Logic is similar in this respect to arithmetic, Whately goes on to say, for there too one is given rules (the algorithms for calculating) which help one more easily to obtain correct results and check the validity of the conclusion. Though Whately does not come out and expressly say so, he undoubtedly believes that a person who can already reason well will be made even more acute through a knowledge of syllogistic logic.
Since the rules of logic help one to avoid fallacies and improve his reasoning ability, they indirectly help to establish the truth in all fields of discourse. However, those who make this the primary aim of logic are misguided. Logic does not help one avoid “the ambiguity and indistinctness of terms” or resolve “doubts respecting the degrees of evidence in various propositions”.
Whately later says that the reason why logic cannot deal with these defects in the first two parts of logic (conceiving, judging) is because indistinct terms and false propositions are still terms and propositions while invalid arguments are not really arguments at all, since no genuine reasoning takes place. Logic can devise rules for distinguishing genuine arguments from fallacious ones, but no formal criteria can be given for excluding the bad terms or propositions. It should be noted, however, that Whately does deal somewhat with the first shortcoming, ambiguous terms, both in his discussion of fallacies and in a special appendix devoted to this topic, which continued to swell throughout the life of the text.
Those who expect this from logic are most unreasonable. It is as if a person would demand that a pair of glasses enable him to read though he had never learned how to do so beforehand.
This illustration most likely came from Copleston.
Those who promise such thing of their systems of “logic” bear the same relation to logic as the alchemists do to genuine chemistry: both hold out fantastic but unachievable hopes to their followers and so by association bring the genuine product into disrepute. This is unfortunate, for logic was never meant to be a panacea for all the intellectual ills of the world. A knowledge of logic is no substitute for other knowledge, but it is still a valuable tool for the limited purpose of reasoning.
As Whately says in concluding his preface:
A knowledge of logical rules will not indeed supply the want of other knowledge; nor was it ever proposed, by any one who really understood this science, to substitute it for any other: but it is no less true that no other can be substituted for this; that it is valuable in every branch of study; and that it enables us to use the knowledge we posses to the greatest advantage.
Before beginning a systematic treatment of logic proper in his “synthetical compendium”, Whately offers his reader an “analytical outline” of logic, starting with the composite whole (reasoning) and analyzing it stages into its elementary components (syllogisms, propositions, terms). The first thing he is keen to point out in this section is that the reasoning process is essentially the same in all argumentation.
In every instance in which we reason, in the strictest sense of the word, i.e. make use of arguments, whether for the sake of refuting an adversary, or of conveying instruction, or of satisfying our own minds on any point, whatever may be the subject we are engaged on, a certain process takes place in the mind, which is one and the same in all cases, provided it be correctly conducted.
Whately makes this principle of “the sameness of the Reasoning process in all cases” the cutting edge in his counter-attack upon the critics of logic on a few specific points, so we should look a bit more closely at what Whately means by it. The main thing Whately wants to assert by this slogan is that there is essentially only one type of reasoning. There are not different varieties of reasoning as common parlance suggests and as some thinkers have actually argued.
Logical reasoning and moral reasoning and mathematical reasoning and so on do not differ in the process or mode of reasoning they employ, but only in their subject matter. Arguments, if they are valid (and Whately takes “reasoning” on the whole to be valid argumentation), can all be analyzed into a common form — syllogistic reasoning. Logic thus studies the conclusive character or structure of reasoning as exhibited in the syllogism.
Logic, which is, as it were, the Grammar of Reasoning, does not bring forward the regular syllogism as a distinct mode of argumentation, designed to be substituted for any other mode; but as the form to which all correct Reasoning may be ultimately reduced, …
This stress, that syllogistic reasoning is a form of reasoning — even that form which makes the validity of the argument manifest — that it should not be taken as a kind of reasoning but as the underlying form of all reasoning, is central to Whately’s outlook.
Though this must surely be how the other defenders of syllogistic logic also viewed the syllogism, they nowhere put the matter as succinctly as Whately does nor did they go on to point out that this is at variance with the view held by logic’s detractors.
Logic no more provides a particular type of reasoning, Whately says, than grammar provides a particular type of language. It instead studies “that mental process which must invariable take place in all correct Reasoning.” Or, as Whately also puts it:
[T]he Logician’s object [is] not to lay down principles by which one may reason, but which all must reason, even though they are not distinctly aware of them: to lay down rules, not which may be followed with advantage, but which cannot possibly be departed from in sound reasoning.
Looking at this issue from the point of view of logic-as-art, one can say that logic provides the requisite tools for testing the validity of any argument whatever. Aristotelian logic, therefore, is not an art of a peculiar kind of reasoning, but is the art of all reasoning.
The above is a first level approximation of what Whately has in mind in saying that the reasoning process is always the same, but we can push our analysis a bit deeper by looking now at what Whately takes the nature of syllogistic reasoning to be. Since syllogistic reasoning is reasoning expressed in its most regular and explicit form, looking at the syllogistic forms should give further insight into this common, underlying reasoning process. This is quite in order, for Whately does think of syllogistic reasoning as being all of a piece. There are, of course, many forms of the syllogism which seem, at least at first glance, to represent quite different modes of inference. But, Whately says, this difference is merely in their form of expression. Underlying or permeating these many moods there is, strictly speaking, only one process of reasoning, one form of inference, taking place. This mental process is captured or summarized by the Aristotelian dictum de omni et nullo, which Whately translates out of Aldrich as: “whatever is predicated of a Term distributed, whether affirmatively or negatively, may be predicated in like manner, of everything contained under it.” Hence this form of inference—passing from an assertion about a class of entities to the “same” assertion restricted to a subclass of entities — is the central (or, to be more precise, the only) type of inference constitutive of reasoning.
Whately is said to have formulated his remarks about reasoning in a much more consciously extensional manner sometimes after 1836.
Whately speaking of this basic form of reasoning in the singular is followed in this thesis, though it could also be considered two form of inference, a negative and a positive one, or even more (to take the dictum as a summary for other first figure moods besides Barbara and Celarent).
Ordinary arguments can be reduced or resolved into a number of regular forms, the various moods of the syllogism, and these in turn can be shown to be nothing more than so many manifestations of the most fundamental form of reasoning.
Whately sometimes seems to speak as if he considers the process of transforming ordinary arguments into syllogistic forms and the process of reducing the different moods to Barbara and Celarent, the most obvious embodiments of the quintessential process of reasoning, to be similar. The various forms of the syllogism differ from ordinary forms of reasoning, it would appear, in their being “regular” and fully explicit in their form.
Whately uses his view of the unity of reasoning to combat those who oppose inductive reasoning to the syllogism. Inductive reasoning, he says, insofar as it is intended to be considered as reasoning, — that is, drawing a conclusive inference from premises, — is potentially syllogistic in form. Whately is at pains to stress this because he thinks that the idea of inductive reasoning being a species of reasoning different from syllogistic reasoning is largely responsible for the notion that the syllogism is merely a peculiar kind of reasoning and so is also responsible for the devaluation of Aristotelian logic by many. However, Whately says, logic recognizes no essential difference between an inductive argument and any other argument.
As an argument induction is best formulated in Barbara, with the base-data being put into the minor premise and an inductive premise made the major. For example, one might conclude that all horned animals have divided hoofs on the basis on having observed sheep, cows, and a number of other like animals having this property. This reasoning process can be formulated in an inductive argument in the following way, according to Whately:
[M] Whatever properties belong to sheep, cows, and various other horned animals [all those examined] belong to all horned animals. [m] All of the sheep, cows, and other horned animals examined have divided hoofs. [C] Therefore all horned animals have divided hoofs.
Whately is said to be following Copleston’s variant of Aldrich’s treatment of inductive arguments here.
Such an argument, Whately notes, is valid, but it is naturally not a proof of the conclusion [C] since the major premise [M] is not known to be true. The truth of the premises in an inductive argument, however, is always beyond the reach of logic and must be established by those familiar with the subject matter of the field under investigation and who are able to judge from experience how representative the cases they have looked at are with respect to the property in question.
Whately treats this qualification as if it relates to the truth or evidence of the major premise. But certainly a naturalist’s intuition would not be expended in establishing this very general proposition, but only a particular case of it, namely, the conclusion itself.
Whately’s analysis of inductive reasoning here is adopted by some logicians, but many of them, including the more prominent logicians of the time, do not accept it. George Bentham disputes Whately’s restricted definition of “reasoning” and claims that inductive argumentation in particular should be thought of as another variety of reasoning. When one asserts an inductive conclusion as highly probable, Bentham says, he might not want to assert the same of the inductive premise which, according to Whately’s account, one is required to assume.
An inductive inference is not usually made by invoking a principle like the uniformity of nature, which is what the induction premise amounts to, but only on the basis of one’s experience with particular things or events.
John Stuart Mill, in his January 1828 article for the Westminster Review, remarks (thought not really in opposition to Whately) that Whately’s analysis of the form of inductive reasoning is an insufficient answer to the inductivist opponents of the syllogism. He himself would prefer to follow out another stress of Whately’s and reject altogether the idea that induction is reasoning. This is, of course, quite different from the well-known position he took later in which inductive inference is made the basis of all reasoning, including deductive.
William Hamilton’s article on logic in the April 1833 issue of the Edinburgh Review sets out 3 sense of “induction” and then proceeds to exclude two of them (induction as investigation and induction as “material illation”, the latter approximately equivalent to what Whately is treating) as being outside the domain of logic. The type of induction which properly belongs to logic, Hamilton argues, is complete induction, which alone is formally valid as an argument. This is often mistaken for a third figure syllogism, he says, because it can be formulated similarly, but it differs from such a form in that it makes use of quite a different copula — “constitutes” or “contains” instead of “is” or “is contained in”.
Inductive reasoning, Hamilton says, proceeds just as most have said, from the parts to the whole, while deduction proceeds in the opposite direction. Whately’s attempt to make inductive reasoning, and a “material” induction at that, identical with syllogistic reasoning is therefore doubly misguided.
Whately does not change his basic approach in later editions, but he does respond to Hamilton’s criticisms (and also to Mill’s 1843 viewpoint) in his 1836 and 1844 editions. In opposing Hamilton’s viewpoint Whately notes that complete induction is rarely used by anyone, while the inductive reasoning process he is treating is of considerable moment.
Finally, Henry Longueville Mansel, following Hamilton, accuses Whately’s view of being an even greater departure (“perversion”, as he terms it) from the true, Aristotelian [that is, Hamiltonian] idea of induction than Aldrich’s. Moreover, he says, Whately’s approach to inductive reasoning “invert[s] the whole operation, stating as a preliminary assumption that which is really the conclusion of the Inductive process.” It also “destroy[s] the whole foundation of reasoning, by commencing with a Syllogism whose premises themselves must be proved by another syllogism, and so on ad infinitum.”
While a number of people disagreed with Whately regarding the nature and form of inductive reasoning, there was nevertheless a fair consensus in favor of his contention that induction and syllogistic reasoning ought not to be opposed to one another.
One cause for this confusion, Whately says, is the fact that many, including “eminent Logical writers”, speak of inductive reasoning as if it were a “distinct kind of argument from the Syllogism”. This, however, is false in Whately’s view. All inductive arguments can be formulated syllogistically. But the most basic cause underlying this opposition is “a vagueness in the use of the word Induction, which is sometimes employed to designate the process of investigation and of collecting facts; sometimes the deducing of an inference from those facts.”
The stress is not in the 1823 edition, but is in by 1827. While Whately’s distinction does clarify the nature of the confusion, he still does not explain why the confusion arose. In Jongsma’s opinion this is of a piece with his failure to see Bacon as a culprit on this issue. The confusion would seem to be related to the way Bacon (and others after him) use the concept of “proof” to include both the process of deducing a result from other, more basic propositions (principles) and the process of exhibiting the empirical or inductive grounds on which a statement is accepted as true. Whately himself is not entirely clear of this terminological confusion, as George Bentham notes in a criticism of Whately’s work.
Whately demonstrates how the multifocal sense of the term underlies the debate by offering the following fallacious “syllogism”:
Induction is distinct from Syllogism: Induction is a process of Reasoning; therefore There is a process of Reasoning distinct from the Syllogism
In the first premise, Whately says, “induction” is taken as a process of investigation, while in the second premise it is taken as argumentation. The conclusion is therefore not warranted, since the middle term — induction — actually divides upon inspection into two different terms. To avoid ambiguity and drawing false conclusions, induction as investigative process must be clearly distinguished from induction as argument. Whately here makes explicit the distinction that lay just beneath the surface in Copleston’s writings.
Though Whately recognizes the legitimacy of logic’s dealing with induction as argumentation, he claims that “as a process of inquiry … it is of course out of the province of Logic.” For, determining the truth of the premises of an argument (which, he says, is precisely what the inductive process does relative to the inductive syllogism) is not something that logic is competent to handle. Logic only deals with the validity of the arguments, not with the certainty or truthfulness of premises.
By 1836, Whately more carefully distinguished induction as argument from induction as reasoning by further emphasizing a point he had made before. An inductive argument, he says, should be thought of not as reasoning by induction but as reasoning from induction.
Induction in this sense is designed to accomplish something quite different than that done by syllogistic reasoning, so it is clear that they are not and should not be opposed to one another. The inductivist logicians’ program of replacing the syllogism with induction, Whately says, is as ridiculous as an agricultural reformer proposing to substitute a plough for a flail in farming. Both are essential for growing and harvesting grain; the one supplements the other. Whately admits that ancient and medieval thinkers tended to neglect induction for syllogistic reasoning, usually improperly grounded, but the modern reaction to this which would see the syllogism done away with in favor of induction alone is no better.
Whately, like Copleston, attributes this opposition between syllogistic reasoning and induction to Bacon’s latter-day followers. He unaccountably holds that Bacon’s pronouncements on the matter are only and quite properly against the excesses of misapplying syllogistic reasoning and in support of a more just view and application of induction.
Whately says: Had Bacon lived in the present day, I am inclined to think he would have made his chief complaint against unmethodized inquiry and illogical reasoning. Certainly he would not have complained of Dialectics as corrupting Philosophy. To guard now against the evils prevalent in his time, would be to fortify a town against battering-rams, instead of against canon.
What Bacon would have done had he lived in Whately’s day is of course a moot point. What he did in his own day, however, is precisely what Whately condemned in other thinkers — he pitted inductive reasoning against syllogistic in the realm of science or certain knowledge.
Whately and Copleston’s complete exoneration of Bacon on this matter seems inexplicable to Jongsma. Whately’s ideas about Bacon have even led R E McKerrow to say that “Two of the important sources for Whately’s notions on logic were Francis Bacon’s Advancement of Learning (1605) and Novum Organum (1620). This view is much more cautiously stated, though not repudiated, in a later work of McKerrow, where it is said that “Whately regarded his own Logic as affirming what Bacon had not meant to deny — the utility of syllogistic logic as a means of assessing consistency among propositions.”
The idea that traditional logic is about consistency (rather than validity, which is quite another matter) is possibly due to W S Howell, who in turn seems to take this characterization over from J S Mill. Howell discusses the history of 18th and 19th century logic throughout his book in these terms.
It should be said, however, that McKerrow’s view of Whately in general, as evinced in his dissertation, his article on Whately and Campbell, and his recent article on Whately’s rhetoric (1982), is at odds with that of Howell.
Whately and Copleston might have said with some justice and a measure of charity that the vulgar opinion about the relation between induction and the syllogism was erroneous and that although Bacon himself contributed to such a viewpoint he should be excused in part because of the times in which he lived. Whately could then have gone to explain why such a view was unacceptable, particularly in the 19th century. But Whately did not take this approach, whatever the reason. Instead he blamed the common sense philosophers Reid, Campbell, and Stewart and, it would seem, their eventual successor in the goal of constructing an inductive logic, John Stuart Mill.
Moreover, his invective increased in intensity as he got older, possibly because he saw the trend slipping away from a purely deductive logic and toward an inductive logic. This new direction in logic becomes especially apparent after the publication of Mill’s System of Logic, Ratiocinative and Inductive (1843), which, like Whately’s treaties, started a flood of new works on logic, only now with the inductive methodology of science considered not only a legitimate but an obligatory concern of logicians. Whately’s response in 1844 to the program of an inductivist logic was to judge it unattainable. At the same time he took the occasion to reassert his own view of the relation between logic and language as the corrective which would keep logic on course.
Whately kept saying that a program of inductive logic does not yet exist and most likely never will.
Whately treats the matter of the syllogism’s role in obtaining new knowledge mainly in the section entitled “On the Discovery of Truth”.
Addressing himself to the question whether one can discover new truths by means of reasoning, Whately first notes that the question requires some prior definition of terms, for this question can be taken in quite different ways and so can lead to seemingly conflicting answers. In the first place, then, “reasoning” must be understood in the strict sense of drawing valid conclusions from assumed premises. Taking a broad definition for reasoning, so as to include induction, for example, would make it irrelevant to the point at hand, namely, whether the syllogism is of any help in acquiring new knowledge. The issue thus turns on the meaning of the terms “discovery” and “new”. Whately answers the question in 2 different ways in turn by considering the question from two points of view relative to the term “new”.
Assuming first of all that by a “new” truth is meant a proposition “neither expressly nor virtually asserted before, — not implied and involved in any thing already known”, one can easily demonstrate that reasoning cannot lead to a new truth. For, Whately argues, since all reasoning is potentially syllogistic in form and since it is of the nature of the syllogism to “virtually assert the Conclusion,” and to “expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out”, it follows that reasoning cannot lead to something that is really new.
Admitting this result, Whately goes on to remark that while the result of reasoning is necessarily implicit in the premises, a person may not always be aware of the consequences which they imply, either because he is not familiar with all the entities to which the premises can be applied, or because it is difficult to keep in mind all the various classes to which a thing can be referred, or even because the person unwittingly holds contradictory views regarding the subject matter presupposed by the premises. Reasoning is thus an effective means “to bring a person to perceive and acknowledge the full force of that which he has admitted”. This is particularly important when the subject matter is complex or abstract, Whately says, for then the implications are less immediate than in other cases.
Shortly after making these remarks, which constitute an appropriate rejoinder, at least in brief, to those critics who claim syllogistic reasoning cannot generate new knowledge Whately proceeds to distinguish between truths or discoveries that are new in an absolute sense — those which “before they were discovered [were] absolutely unknown, being not implied by any thing we previously knew, though we might perhaps suspect them as probable;” — and truths or discoveries that are only relatively new — those “which may be elicited by Reasoning, and consequently [are] implied in that which we already know”. Whately terms the first type of discovery “physical discovery” (without intending to restrict it to physical science, however) and says that such discoveries result in new information in the strictest sense of the term. The other type of discovery he calls “logical discovery”; it makes explicit what was implicit in knowledge that had already been acquired. Knowledge of the first kind is gained through observation or through the testimony of others and can be characterized as “information”; knowledge of the latter type is gotten by reasoning and can be considered “instruction”.
I am made to think here that logical discovery entails instructions which in a sense means information processing done using rules as in a computer.
These two classes of discoveries are naturally not mutually exclusive, Whately says, for what is a “logical discovery” for one may be only a “physical discovery” for someone else. And, he adds, this is usually the case whenever a general law is involved, for they must be established through reasoning, but many will not be equipped to know such a proposition on the basis of what they already know.
If a person does not know a given result prior to learning that it is true, the status of that result as a discovery depends both upon his fund of knowledge and upon the method by which he learned it. If, however, he can deduce it from what he already knows, it will be a “logical discovery”. If he learns of it through a process of reasoning, the premises of which he knows to be true, the result is a “logical discovery”. If, on the other hand, he sees that the result follows from principles which he is unacquainted with, it will be merely a “physical discovery” for him until he becomes convinced of the truth of these premises.
It is important to distinguish between these 2 types of discoveries, according to Whately, but both kinds are still discoveries of new truths in the ordinary sense. A “logical discovery” is no less important than a “physical discovery” for extending one’s knowledge; only the process of acquiring the truth is different.
One might compare this process of acquiring new truths to the case in which a man has a hidden vein of metal in his property. Strictly speaking, he owns this vein, but until it has been brought to light, it is to all extents and purposes not his metal at all. Discovering that he possess this vein of metal is of course still different from purchasing an estate which is already known to contain a metal deposit, but in both cases there is a real sense in which the man gains a new possession.
In this analogy and others like it, Whately implicitly distinguishes between a result’s being logically contained in or implied by the premises (the buried metal) and its being made evident to the reasoner through the derivation, which constitutes or produces the actual knowledge of the result (unearthing the metal).
Had he gone on to explicitly pinpoint the source of the confusion in this manner and to explain how a proposition can be logically implied by other, already known propositions and yet not be known itself, even further clarification of the issue would have ensued. But Whately was still a bit timid, it seems, in asserting the epistemic value of deductive reasoning. A distinction such as that between a valid argument and a fully rigorous (gapless) deduction seems not to have occurred to him.
Though Whately stresses throughout his treatise that the subject matter of logic is valid argumentation and not proof or truth, he seems to mean by this both that the arguments are valid and that they are deductions. His distinguishing arguments from syllogisms seems to approach the distinction between valid arguments and deductions, but this distinction may be on a psychological level, the syllogisms being the ones that are obviously deductions and the arguments being that are not so obvious. He does not clearly distinguish valid arguments and deductions in a logical sense, though there was ample opportunity for him to do so relative to the axiomatic theories in existence at this time (Euclidean geometry and Newtonian mechanics). As for making this distinction among syllogisms, Whately fails even to state what the difference is between perfect and imperfect terms (something is missing here) distinguish those moods (the first figure syllogisms) that clearly exhibit the basic process of reasoning in their very form from those that still lack complete perspicuity.
Yet he does refer the reader to mathematics and notes that the theorems of geometry are all contained in or implied by the axioms and definitions, but that they are not for all that any less instances of new truths gotten by reasoning. The theorems may have been conjectured or “discovered” in another way, but until they are shown to be based on previously established results, they are strictly speaking not knowledge at all. Whately defines knowledge as “firm belief of what is true on sufficient grounds”. Whately does not take mathematics as a decisive illustration of his point, though. This could be because mathematics was not foremost in Oxford’s educational system or his own background; or it might be that his view of mathematical knowledge as arising out of the meaning of the terms, makes him think of it as not being a particularly striking illustration of his point. Whately’s viewpoint on the nature of mathematical knowledge is derived principally from Dugald Stewart. He, like Stewart, considers mathematics to be a “hypothetical” science; that is, a science in which the basic principles of mathematics are “hypotheses”, or what we might call “postulates” — they are not axiomatic truths. The theorems or propositions of mathematics are thus true only in the sense that they “conform” to the first principles laid down.
I wonder how conformity to first principles and conformity to axioms are different here. This could be in a manner that Whately sees mathematics as following intuition rather than being close to Platonic forms which are studied. In this manner, it is not akin to the unchallengeable laws of thought, but rather something that follows from laws of thought. Laws of thought being one rank higher than the intuitionally moulded/kneaded mathematical concepts. Concepts are hypothetically postulated and whole rubrics of mathematics is then constructed in a way that follows the principles laid down.
Mathematical results, though certainly not trivial, appear to him to be derivable in a relatively straight-forward manner, so they would not illuminate his point as well as those of some other field.
Whately says that mathematical truths are in the class of “logical discoveries” because “to him who properly comprehends the meaning of the Mathematical terms, (and to no other are the Truths themselves, properly speaking, intelligible) those results are implied in his previous knowledge, since they are Logically deducible therefrom.’ He does say that there is definitely “call for skill in the selection and combination of the Premises” to construct an actual demonstration and that the result may well be “a new, that is, unperceived and unthought-of Conclusion” and that to make discoveries from premises long known by everyone requires a “master mind”.
Whately’s reviewers George Bentham and John Stuart Mill are not as bashful about asserting the usefulness of deductive reasoning for gaining new knowledge, particularly with respect to mathematical science.
John Stuart Mill and George Bentham were good acquaintances. Mill was a close friend of the Bentham relation and stayed with George’s family about a year in France (1820/21). In 1825 Mill was engaged in editing Jeremy Bentham’s Treatise Upon Evidence. George Bentham was involved in a similar task on his uncle’s logical writings; the 1827 treatise which he wrote on logic drew heavily from these manuscripts in its positive outlook, thought it contained original ideas of his own as well, most notably the controversial doctrine of the “quantification of the predicate”.
Bentham disagrees with Whately that all reasoning is essentially syllogistic, but he does not therefore degrade deductive reasoning like most of the earlier critics of logic.
He claims that “new truths can be, and actually are, elicited by syllogistic reasoning.” If, he says, one discovers for the first time ever a mathematical result such as ‘all equilateral triangles are equiangular’ by means of “reasoning, and by that alone, (which was probably the case with the mathematician who did discover it); is not this discovery … as new as the first discovery of any unknown real object?”
Now, to be fair to Whately, we should say that this view does not really contradict Whately’s outlook, for Bentham is definitely not asserting that syllogistic reasoning can deduce consequences which are not implicit in the premises. He wants instead to underscore the fact that given the normal notion of “new truths” one is rightly entitled to assert that syllogistic reasoning generates new truths from old ones. Whately’s stimulative definition of “new truth”, Bentham says, is a distortion and one which he himself does not always adhere to in his work, as he later seems to repent of it.
Bentham, it seems to Jongsma, is being a little obtuse here in order to find something to criticize in Whately’s position. Granted, Whately’s discussion is not as well-organized or as clear as it could have been, but with a little effort Bentham should have been able to puzzle out Whately’s meaning and note the shifts in his argument.
Furthermore, Whately’s first considering the restricted notion of “new” is quite germane to the issue at hand, for the critics of logic take the syllogism’s soundness in being able to derive only conclusions implicit in the premises to entail that it must therefore be epistemically impotent. Whately may have bent over a bit too far to answer the critics’ arguments, but he is certainly not guilty of gross ambiguity on this point.
Mill’s article, which appeared anonymously about a year later, interprets Whately more faithfully on this matter, but it reaffirms the utility of deductive reasoning for mathematics and physical science in even stronger terms.
John Stuart Mill said of Whately’s idea on unfolding the particular propositions held out in the general as:
Metaphysicians have found it a very difficult problem, to explain on philosophical principles this seeming paradox; to prove that possible, which experience certifies to be true; that mankind may correctly apprehend and fully assent to a general proposition, yet remain for ages ignorant of myriads of truths which are embodied in it, and which, in fact, are but so many particular cases of that which, as a general truth, they have long known. We do not think that our author has advanced much nearer than his predecessors to the solution of the mystery: but he has illustrated the fact itself most elegantly and instructively; and that person must be far advanced in this kind of knowledge, who can read the chapter without deriving from it an important addition to his stock of valuable ideas.
Reading this part of Whately’s logic was apparently a “learning-experience” for the 21 year old Mill, if we are permitted to interpret the last sentence of this passage as a personal testimony. If so, every teacher deserves such a pupil to popularize his viewpoint. For by condensing Whately’s ideas and drawing specific and singular attention to their application to mathematics and physics, Mill enhances Whately’s position. Moreover, in an earlier passage, Mill goes so far as to correct Whately’s perception of the intellectual faults of medieval thinkers. Whately (no doubt following Copleston and Gillies), had asserted that logic had been perverted by various philosophers in making it out to be an engine of science. But, Mill says, their fault lay not with using syllogistic reasoning for obtaining new results, but in not paying sufficient attention to the process of acquiring the fundamental propositions from which they reasoned. With respect to the reasoning process itself, their practice is no different than that of modern scientists.
Mill notes:
[M]odern philosophers have operated (though with more success) in the very same mode which the schoolmen attempted: they have ascertained by induction certain very general facts; the laws of motion, that of gravitation, of the reflection and refraction of light, &c. and have deduced from these, by a series, sometimes a very long series, of syllogisms, innumerable conclusions with respect to past, present, and even future, physical facts. Surely it is time that the practice of reproaching the schoolmen for doing precisely what we do ourselves, should cease.
Mill continued to be perplexed by the matter of how or why deductive reasoning leads to new knowledge, until he “resolved” it later to his own satisfaction in the 1843 Logic by interpreting syllogisms and universal proposition inductively.
Autobiographical and Literary Essays. Collected Work of John Stuart Mill. Volume 1. Edited by John M Robson and Jack Stillinger 1981 The Development of John Stuart Mill’s ‘System of Logic’ — Oskar Alfred Kubitz 1932
Though, he protested calling logic an organon or engine of science, Copleston had in fact stressed this very point with respect to Aristotle — that modern and ancient philosophy, including natural philosophy, are identical in logical structure or approach. Whately adopted the one but seems not to have picked up the other.
Whately does not alter his discussion of the role of the reasoning in discovering new truths after various reviews of his Logic were published. But by 1844 he adds a few comments that both explain how one might not realize the implications of what he has assumed or already knows and why people might conclude that syllogistic reasoning is nugatory. Apropos of the first point, Whately merely reiterates in a more explicit, symbolic fashion what he had said earlier; namely, that in proving that a certain property can be predicated of a particular species of entity, the subject matter may be so complex that it may not be immediately evident that the conclusion follows from the premises. Whately still does not (and never does) point out that the complexity of the argument-form may contribute to the difficulty in seeing that a result follows from its premises. He treats the issue in terms of the simplest form, Barbara and so has recourse to the subject matter alone in locating the problem.
The critics of logic, encouraged by the example of textbook writers, have usually taken trite examples of reasoning as the basis for their analysis, supposing that what they have to say about them apply to all cases of reasoning whatever. Considering only cases in which the consequence is obviously implied by the containing premise to anyone who understands the meaning of the terms involved, they conclude that all syllogistic reasoning is merely trivial particularizations of one of its premises and so cannot lead to new knowledge. But, says Whately, consider instead a case in which genuine mental exertion is involved in separately ascertaining the two premises and in which both premises clearly contribute to establish the conclusion. Take the example, he says, of some men who dig up the skull bone of an animal that was obviously horned. Unless they are knowledgeable naturalists, they will not be able to conclude from this that the animal was once a ruminant. On the other hand, a naturalist who hears about the find but does not learn that the skull is from a horned animal will also not be able to conclude that the animal was a ruminant. One must know both premises in order to draw this conclusion. This is true of all syllogisms: “when the two premises [of an argument] are combined, they do, jointly imply and virtually assert the conclusion; though, separately, neither of them does so.” One might say (though Whately doesn’t) that reasoning is the chemistry of propositions — given two separate premises, their conclusion is not yet derivable, but combining them correctly through reasoning, yields the result. One need not know the conclusion or see that it is true until the argument is constructed. This is especially true when the connections among the various terms involved are not obvious. Reasoning may then be aptly compared to computation with large numbers. Knowing that two quantities are such and such, one “has virtually asserted that the sum-total is so and so; and yet the readiest accountant requires, in this case, some time to bring these items together before his mind [that is, to determine the sum of the addends].”
Here Whately could have pursued the analogy further to distinguish valid arguments (the addends with their sum) from deductions or proofs (the computation which shows that the stated sum is correct or follows from the addends). He then could have said, keeping mathematics in mind as an example, that the premises containing their conclusion does not mean that the conclusion is better known or more evident than the premises. This would have shown that the reason normally given by logic’s critics for why the syllogism cannot lead to something new is at best insufficient for supporting the argument.
Whately’s discussion of the epistemic productivity of reasoning is formulated in rather general terms regarding the discovery of new truths. What he says obviously applies to Kames’ and Campbell’s criticisms, though he himself does not spend much time doing so. Kames is not even mentioned in this context, and Campbell’s petitio principii charge is discussed here more or less in passing.
It is interesting to note that Whately addresses the matter of “discovering new truths through reasoning” instead of “syllogism’s deriving better known and more particular propositions”. The latter way of talking is how Kames and Campbell and Stewart (on the whole) present the issue. The former way, though it may be mere coincidence, is how Lyall (briefly) discusses it in reaction to some statements of Stewart. Whately does not, however, adopt Lyall’s specific explanation for why people find the criticism sound; he at most thinks of the issue in some of the same terms.
Whately answers Kames’ remark that Aristotle argued like a normal human being instead of using syllogistic reasoning in the introduction by saying that the syllogistic form is not a type of reasoning, but only the regular, expanded form into which all reasoning can be analyzed: “as well might a Chemist be charged with inconsistency for making use of any of the compound substances that are commonly employed, without previously analyzing and resolving them into their simple elements; as well might it be imagined that, to speak grammatically, means, to parse every sentence we utter.”
It seems that Campbell is the principal antagonist in Whately’s “Analytical Dialogues”, rating some rather strong language. His work still figures prominently in the Logic as well, but Whately addresses Campbell’s arguments more calmly there. Besides dealing with the circularity charge, Whately discusses Campbell’s criticism that syllogistic reasoning is ill-fitted for “moral reasoning”. On the basis of his own interpretation of inductive reasoning, Whately criticizes Campbell’s view as erroneous because it overlooks the fact that a merely probable induction-premise communicates its degree of uncertainty to the conclusion.
Whately’s reply to Campbell is balanced somewhat on both sides of the issue. Assuming his own view of the nature of reasoning and the role of the syllogism, Whately notes first of all that Campbell’s critique applies not only to the syllogistic form of reasoning, but to reasoning in general. This, Whately says, should have caused Campbell to rethink his charge, for if true, it sabotages all reasoning whatsoever, including Campbell’s own arguments about the futility of the syllogism. This criticism Jongsma thinks is strongly reminiscent of both Kirwan’s and Lyall’s.
The fallacy of petitio principii is classified by Whately as a non-logical or material fallacy; that is, the conclusion follows from the premises (the argument is valid) but the premises have no right to be assumed. Petitio principii is thus a fallacy of demonstration as opposed to one of mere deduction. The conclusion is fairly deduced, but the premises themselves cannot be known unless the conclusion is known. This fallacy occurs, says Whately, in “those cases in which the Premiss either appears manifestly to be the same as the Conclusion, or is actually proved from the Conclusion, or is such as would naturally and properly so be proved”. A closely related material fallacy, he observes, is the one of “undue assumption of premises”. This is the fallacy of arguing from premises that are themselves still in question. Arguments based on premises that are less evident than the conclusion form a class within this category.
Whately remarks that a syllogism may appear fallacious in one of these two ways, either by assuming a premise which is less evident than the conclusion or by assuming a premise which can be proved from the conclusion. Yet such syllogisms need not be fallacious, so long as no circular reasoning ensues; that is, so long as the premises can be fairly proved by some other means.
It is to be observed, however, that in all correct Reasoning the Premises must, virtually, imply the conclusion; so that it is not possible to mark precisely the distinction between the Fallacy in question [petitio principii] and fair argument; since that may be correct and fair Reasoning to one person, which would be, to another, begging the question, since to one the Conclusion might be more evident than the Premiss, and to the other, the reverse.
This passage deserves several comments. In the first place, Whately here blurs the very thing he makes a point of clarifying later on in the work. The evidence of the premises is not (directly) at issue in the fallacy of begging the question, though it may be in unduly assuming the premises. A petitio principii is committed, according to the definition Whately gives, when one of the premises is logically posterior (in the order of knowledge) to the conclusion, not when the conclusion is more evident or epistemically prior to one of the premises (which is what Kames’ and Campbell’ criticisms assert). That Whately continues to propagate this confusion in the context of discussing the charge that the syllogism is a petitio principii is the more to be regretted, for it permits a wrong and indistinct notion of the accusation to go unchallenged. Whately thus missed a capital opportunity of straightening out both the terminology and the real nature of the accusation being levelled.
This passage seems to be at variance with his definition of petitio principii in another way as well. Whately here individualizes the order of knowledge, for he says the premises may be more evident than the conclusion to one person, so that the augment serves as a proof for him, while it may be quite the contrary for someone else. But in defining the petitio fallacy Whately talks as if there is a common, fixed order of knowledge — which is certainly a more standard Aristotelian (and early modern) way of viewing knowledge.
Jongsma notes that he doesn’t know if Whately is one of the first to relativize the order of knowledge or not, but he suspects that it goes against the general view of his time, particularly of those who reflect on the nature of the scientific enterprise.
Regardless of whether Whately held contradictory ideas on this matter when he first wrote his Logic, the relativized version of the order of knowledge, which also underlies his 1823 discussion of discovering new truths by means of reasoning, was the one he adhered to in the end. By 1844 Whately adds some parenthetical remarks to the passage in which he defines the petitio fallacy which show that he does not want to be understood as advocating a fixed order of knowledge. After saying that the question is begged when one of the premises is “actually proved from the Conclusion, or is such as would naturally and properly so be proved”, Whately says, “i.e. such as the persons you are addressing are not likely to know, or to admit, except as inferred from an admission of the Conclusion”, noting “it should be remembered that of two propositions, the one may be the more evident to some, and the other, to others.”
Whately’s response to Kames’ and Campbell’s charges, then, may be summarized in the following way. Because “proof” and “knowledge” are relative to each person’s given state of knowledge, one cannot say that a given syllogism does or does not beg the question or proceed in the wrong direction epistemically. But the charges advanced are wrong as stated, since they assert that this is so in general. It is true that certain syllogisms, genuinely offered as demonstrations, will be epistemically defective for some people, but this does not make the syllogism fallacious. Moreover, this flaw is not peculiar to the syllogism; it holds true of reasoning in general. The stated accusations, then, besides being strictly false, are also misguided in singling out only the syllogistic form of reasoning for criticism.
Whately seems to have accepted the criticism more at face value in his “Analytical Dialogues”, if McKerrow’s assessment of 1976 is correct.
Campbell and Whately on the Utility of Syllogistic Logic — McKerrow (Winter 1976)
Whately’s arguments in support of the utility of syllogistic reasoning form the crux of his defense of Aristotelian logic. However, Whately also responded to some of the more technical criticisms that had been brought up by Reid and repeated with some variation by Stewart. We will look first at what he says (and fails to say) about the quasi-mathematical canons and the general rules of logic and then at his defense of the Aristotelian dictum.
Perhaps the only thing which needs to be said about Whately’s treatment of the canons or axioms, which he takes over from Aldrich, is that it completely ignores the criticism that had been leveled at it by Reid and accepted by Gillies. He treats the canons as if they are simply part of the systematic development of logic agreed to by all. It would appear, then, that there is nothing much for us to relate concerning Whately’s view of the canons relative to his defense of logic. But even if this were so, his technical presentation of the canons is interesting for what it reveals about the level of understanding which existed at the time and earlier among logicians, so we would still make a brief remarks about his approach. But what Whately says about the syllogistic rules that are based on the canons may be considered as tantamount to an answer to another criticism of Reid, so his ideas on the canons are not totally irrelevant to our main concern.
According to Whately the canons serve two functions. They first of all state the fundamental laws underlying all syllogistic forms of inference. They are, he says, “the axioms or canons by which their validity is to be proved” — “for no Syllogism [“categorical syllogism” in 1827 work] can be faulty which does not violate these canons.” The canons can be applied directly to show the validity of any categorical syllogism, he says, while the Aristotelian dictum applies directly only to moods in the first figure. In making these assertions, Whately shows that he, like others of his time, believes that showing that certain moods are not proven to be invalid is the same as demonstrating their validity, which, as we have noted in the opening section of the first chapter, is not warranted without further argument.
Besides claiming that the canons can be used to show validity, Whately asserts that the Aristotelian dictum can be used to show invalidity of arguments. If one cannot put an argument into the requisite form, then the argument cannot be valid. This outlook must be the basis for Whately’s remarks, for he nowhere argues the point in any other way, nor does he show in what sense the various valid moods are to be considered applications of the canons.
The second function of the canon is to derive general rules by which invalid syllogistic forms can be excluded. Here Whately presents 6 of Aldrich’s 12 rules, giving loose arguments for them that appeal to the canons.
After doing this, he then uses the rules to reject various moods as invalid, almost exactly as Aldrich had done. The canons, together with the derived rules, thus serve to establish invalidity in (not unsurprisingly) all cases but the valid argument forms.
Reid, it will be recalled, thought that this “modern” process of establishing invalidity was pseudo-scientific, partly because he disputed the axiomatic character of the canons for logic. He may possibly have preferred Aristotle’s approach of using counter-examples, although he mocks the cryptic way in which Aristotle presents his examples. What Whately says about detecting fallacies or particular invalid arguments is quite relevant to this matter. To show that a given argument is invalid, Whately says, one can often formulate another one exactly corresponding to it in form but in which the premises are true and the conclusion is false. This demonstrates the invalidity of the original argument. Whately, as well as his mentor Copleston, used this approach very effectively in arguing against logic’s critics, as we have seen several times above. But it would really be better and more “scientific”, Whately says, to show that an invalid argument cannot be reduced to the basal form of all reasoning or that it violates some rule of logic.
This mode of exposing a fallacy, by bringing forward a similar one whose conclusion is obviously absurd, is often, and very advantageously, resorted to in addressing those who are ignorant of Logical rules; but to lay down such rules, and employ them as a test, is evidently a safer and more compendious, as well as a more philosophical mode of proceeding.
Now Whately does not consciously address these ideas to the charge that using rules to exclude invalid argument forms is pseudo-scientific, but without bending Whately’s, outlook in the least, it can be considered as his position on the issue, providing as it were an after-the-fact rationale for the practice.
The technical criticisms that Whately mainly deals with relate to the Aristotelian dictum, which is, according to Whately, the underlying form of reasoning and which plays a central role in his logic. There are two criticisms which he takes up, the first one being the rather minor one regarding its “dignity” or scientific value, and the second one regarding its precise role in establishing the validity of the syllogistic forms of reasoning. Both of these seem to be addressed in the form given them by Stewart in his 1814 work on logic, though they originate with and are partly quoted from Reid.
Reid and Stewart had derided syllogistic logic as being rather trivial because all the many forms of the syllogism were based on (were particular applications of, as they say) such a simple axiom as the Aristotelian dictum. Whately, possibly following Lyall, finds this attitude incomprehensible.
Lyall does not mention the Aristotelian dictum but he does express the same idea regarding the value and goal of axiomatizing logic.
Whately says:
It is not a little remarkable that some, otherwise judicious writers, should have been so carried away by their zeal against that philosopher [Aristotle], as to speak with scorn and ridicule of this principle [the Aristotelian dictum de omni et nullo], on account of its obviousness and simplicity; though they would probably perceive at once, in any other case, that it is the greatest triumph of philosophy to refer many, and seemingly very various, phenomena to one, or a very few, simple principles; and that the more simple and evident such a principle is, provided it be truly applicable to all the cases in question, the greater is its value and scientific beauty.
If Reid and Stewart had come to logic with an open mind, Whately says, “instead of ridiculing Aristotle’s principle for its obviousness and simplicity, [they] would have perceived that these are in fact its highest praise: the easiest, shortest, and most evident theory, provided it answer the purpose of explanation, being ever the best.”
The second criticism of the Aristotelian dictum which Whately counters is the one of Stewart and Reid regarding the senselessness of demonstrating the various syllogistic moods.
Since Reid and Stewart differ somewhat on this point and since Whately’s answer is less than perspicuous, we will first quote Whately at some length to see both what criticism he is responding to and what his reply is. Then we will make some interpretative and critical comments of our own.
The same writer [Stewart] brings an objection against the dictum of Aristotle, which it may be worth while to notice briefly, for the sake of setting in a clearer light the real character and object of that principle. Its application being, as has been seen, to a regular and conclusive syllogism, he supposes it intended to prove and make evident the conclusiveness of such a syllogism; and remarks how unphilosophical it is to attempt giving a demonstration of a demonstration. And certainly the charge would be just if we could imagine the Logician’s object to be, to increase the certainty of a conclusion which we are supposed to have already arrived at by the clearest possible mode of proof. But it is very strange that such an idea should ever have occurred to one who had even the slightest tincture of Natural Philosophy: for it might as well be imagined that a Natural Philosopher[’s] or a Chemist’s design [is] to strengthen the testimony of our senses by a priori reasoning, and to convince us that a stone when thrown will fall to the ground, and that gunpowder will explode when fired, because they show that according to their principles those phenomena must take place as they do. But it would be reckoned a mark of the grossest ignorance and stupidity, not to be aware that their object is not to prove the existence of an individual phenomenon, which our eyes have witnessed, but (as the phrase is) to account for it; — to refer, in short, the individual case to a general law of nature. The object of Aristotle’s dictum is precisely analogous: he had, doubtless, no thought of adding to the force of any individual syllogism; his design was to point out the general principle on which that process is conducted which takes place in each syllogism. And as the laws of nature (as they are called) are in reality merely generalized facts, of which all the phenomena coming under them are particular instances; so the proof drawn from Aristotle’s dictum is not a distinct demonstration brought to confirm another demonstration, but is merely a generalized and abstract statement of all demonstration which (mutatis mutandis) accommodated to the various subject matters, is actually employed in each particular case.
Whately views the criticism as relating to particular arguments. He looks at the criticism as saying two different things; that the procedure in question makes the conclusion more certain than it was before the argument was shown to be valid, and that it proves the validity of an argument already known to be valid. He thus rejects the criticism as ignorant, for Aristotle surely knew that if a conclusion was certain or known to follow from the premises by means of a syllogism, no further proof of the argument’s validity would strengthen the argument’s conclusive character or the result’s evidential character. Now, though Stewart’s comments are couched in terms of the conclusiveness of particular syllogism and the certainty of their conclusions, yet the criticism is surely meant to be aimed at the reduction process which establishes the validity of various argument-forms.
It is not clear that Whately thought of them as two different things, for he passes from the conclusiveness of an argument right into the certainty of its conclusion without pausing to shift gears.
The argument of Whately quoted above shares certain features with that of Lyall particularly the failure to explicitly relate the criticism to the reduction process, concentrating instead on the validity and evidence of particular arguments. Jongsma does not know whether Whately took over Lyall’s viewpoint on Stewart or whether he came to it independently, but he does not think that a close reading of Stewart will bear up their interpretation of what is at stake in the criticism.
Whately thus ought to have clarified precisely what procedure the criticism related to and answered it from that vantage point. That he did not may indicate some ambivalence on his part regarding the actual role to be played by the Aristotelian dictum and by the reduction process.
In the second place, then, we should analyze how Whately looks at the Aristotelian dictum over against the various syllogistic moods. He says in the above passage that the dictum exhibits the principle on which all argumentation takes place, that it accounts for its conclusiveness or validity. This is because at heart all reasoning is conducted according to the one basal and universal rule of inference summarized by the dictum. All valid arguments, syllogistic in form or not, are embodiments or particular exemplifications of this underlying form. Whately says that all actual arguments are “applications” of the Aristotelian dictum, though he notes elsewhere that by this one should not understand that they are arguments in the same form, (so that strictly speaking the Aristotelian dictum is not a generalization of all syllogistic forms), for some arguments are direct applications (the first figure moods) while others are not immediately so but require first to be resolved or reduced into one of the first figure moods. But granting that the dictum “may be ultimately applied to all Arguments”, what is it that this application does? What, in particular, does reduction accomplish? Whately does not say much about the purpose of reduction except to say that it transforms syllogistic arguments into the form “prescribed by the dictum of Aristotle”. It is thus the last step in the process of resolving or reducing an ordinary argument into its elementary or strict logical form, so making its conclusiveness perspicuous. As such, however, it must also show the argument’s validity. Whately distinctly speaks of the dictum proving the validity of an argument, of the validity of an argument resting upon the dictum. Yet he is hesitant to concede this point when he is discussing Stewart’s criticism. The most he will say there is that the dictum somehow accounts for the validity of the various arguments, intimating that it does not make evident an arguments’s validity. Why? The only explanation Jongsma can offer is that Whately was not completely convinced of the need to show the validity of the syllogistic forms of reasoning. It seems that he also thought of these forms as complete deductions whose validity need no demonstration. A syllogism, he claims, is “a valid argument, so stated that its conclusiveness is evident from the mere form of the expression”. If this is so, what would a reduction accomplish? If it is immediately evident (a self-evident truth) that all syllogistic forms are conclusive, then they would all seem to be equal as rules of inference. Reduction should therefore not be used to show that the validity of certain primitive forms establishes the validity of others.
Whately seems to be caught on both sides of the question, “Does the Aristotelian dictum demonstrate the validity of the various syllogistic moods or not?” Whately might have stopped vacillating by distinguishing between demonstrating that a mood is valid and its actually being valid. He could have then said that the process of reduction does show or make evident that these moods are valid, but that it doesn’t make them valid or increase their validity. Stewart’s criticism that the procedure is calculated to fortify syllogistic argumentation can be rejected without denying Reid’s analysis. Asserting that Reid’s analysis is correct but that it is nothing to be concerned about and is no criticism of logic would have dispelled the fog that surrounded this issue. Even at this, however, he would still need to puzzle out why reduction is necessary at all if the canons have already established validity, and why logic should have two unrelated sets of basic principles, the Aristotelian dictum which applies to first figure moods, and the canons which apply, as he thinks, to all moods. Reflection on these points, too, might have served logic well and would in any case have contributed to the discussion which occurred later regarding which principles were to be accepted as axiomatic in logic.
Actually, according to Whately, both sets of principles (the dictum as well as the canons) can be used for both, as we noted above.
We will first look at how a few of his contemporary British critics and reviewers viewed the work. We have already incorporated a number of their specific criticisms regarding the various issues treated by the work, so we will restrict our attention here to their more general evaluations of the text. Following that, we will conclude with an appraisal of the nature and importance of Whately’s work in the context of the history of British logic.
Facsimile Reprint of George Bentham 1906 — Benjamin Daydon Jackson 1976
George Bentham, who was at work revising his uncle Jeremy Bentham’s manuscripts on logic at the time, read Whately’s logic and decided to write a book-length review of it. It is in this work that the theory of the quantification of the predicate and the notion of propositions being equations are first introduced into British logic.
Quantification of the Predicate and Many-Sorted Logic — William Tuthill Parry March 1966
Bentham’s work is entitled Outline of a New System of Logic, with a Critical Examination of Dr. Whately’s ‘Elements of Logic’. The title reveals the work’s dual purpose. On the one hand Bentham intended it to serve as an introduction to his own system of logic as based upon his uncle’s ideas. On the other hand it was organized according to Whately’s treatise and was meant as a detailed answer and appraisal of it. That Bentham rushed his ideas into print without first developing them into a complete system of logic — something he promised he would do later, but never did — and that he concentrated wholly on the Elements of Logic in doing so reveals the importance he attached to Whately’s work. He views Whately’s Logic “as the last and most improved edition of the Aristotelian system”. Hence, in presenting his views over against Whately’s, he feels that he is addressing “Aristotelian Logic in general” rather than merely one particular system of logic.
Bentham’s reaction to Whately’s defense of syllogistic logic, which is our concern here, can be summarized by saying that on the positive side he appreciated both Whately’s discussion of the utility of logic (insofar as it could be considered the science and art of reasoning) and his demonstration that deductive reasoning does have epistemic value after all — though, as we saw, he was not completely fair in assessing Whately’s position on this matter. On the negative side, however, Bentham liked neither Whately’s position on the scope of logic nor his ideas on the nature of reasoning.
Logic, Bentham says, is “the branch of art-and-science which has for its object the advantageous application of the human mind to the study of any other branch of art-and-science.” Its sphere of action is not restricted to the forms of transmitting knowledge; logic should also show how knowledge can be acquired. Logic does not include anything particular to a given subject, but treats “such [rational] modes of proceeding as are universally applicable to art-and-science, whatever be the subject matter in question.” To narrow logic down to a study of reasoning limits logic far more than it ought to be. Other intellectual operations, such as classification, also fall within its scope.
Moreover, Bentham continues, the “ratiocinative” portion of logic should treat any form of rational inference from premises to a conclusion, not merely conclusive reasoning, as Whately would have it. Both deductive and inductive forms of reasoning are properly within logic’s purview, and they are quite distinct. Whately’s supposed reduction of inductive arguments to syllogistic ones is completely unacceptable. Deductive or conclusive argumentation, is valid argumentation from principles that are “regarded as absolutely true,” what we would call “proof” or demonstration. Deductive reasoning is therefore useful for advancing to new truths from ones already derived. It is also extremely useful in analyzing given arguments to determine whether they are valid or not. An argument is inductive, according to Bentham, if it is not such a demonstration — “Whenever it contains doubtful propositions, or when the absolute truth of one proposition [the conclusion] does not follow from the exhibition of the others [the premise]”.
Bentham’s division of argumentation into deductive and inductive reasoning is clearly not made on the basis of the form of the argument. According to this rather unusual classification, all valid arguments proceeding from premises not known to be true, including reductio ad absurdum arguments in mathematics, Jongsma supposes, would have to be termed inductive arguments.
Yet though an argument may not be totally conclusive, Bentham says, there often is sill “a certain degree of reasoning [taking] place”. Such inductive arguments are important for acquiring new knowledge in fields of thought where absolute certainty is not attainable. For such cases logic should lay down rules to help determine when inductive inference is properly performed and when it is not. It should enable one to decide what “degree of probability” or “degree of universality” ought to be attached to the conclusion of a given argument. The topic of evidence, then, which Whately ejected from logic, is on the contrary quite properly part of logic’s concern, even if it has no part to play in the deductive branch of the theory of reasoning.
Bentham’s quarrel with Whately can be viewed as largely a debate over words — what “logic” and “reasoning” ought to mean. But it is of course not only that. It relates to whether Aristotelian logic can in a natural way be considered a part of logic in Bentham’s sense, whether reasoning, with all its reputed value, should be extended to cover a variety of argument forms, regardless of the nature of the connection between the “premises” and “conclusion”. The outcome of the debate had practical consequences, for the argument was not merely how to use words, but, for example, what sorts of things ought to be emphasized and taught in the university’s curriculum and what sorts of things were important for scientists to know. Bentham’s position on these things presaged the state of things to come; in particular, there seems to be a certain affinity between some of his ideas and Mill’s later ideas on logic.
Mill’s review of Whately’s Elements of Logic in the January 1828 issue of the Westminster Review was much more congenial than Bentham’s. Having just studied Whately’s logic in conjunction with some other traditional logics during 1827 and being aware of the various criticisms of syllogistic reasoning, Mill could appreciate the value of what Whately had accomplished for logic. Mill did offer a number of criticisms of Whately’s work, some of a more minor or technical nature, some intended to further Whately’s arguments, and some to supplement or modify his outlook, but these were tendered in a genuine spirit of constructive criticism. His reservations about Whately’s work did not lessen his admiration for its merits, and the review shows a good understanding of the nature and aim of the treatise.
Whately’s work, Mill notes almost at the outset, is better considered a treatise in philosophy of logic than in logic itself.
Mill agrees with Whately that all reasoning is potentially syllogistic in form, including inductive reasoning; that the syllogism is not a particular kind of reasoning but merely its regular, expanded form; that it is often useful to put arguments into this form in order to test them for validity and detect fallacies; and that deductive reasoning can be and is useful for advancing scientific knowledge.
Mill, like so many others of his age, thought that Whately’s circumscribing logic as a theory of reasoning was far too restrictive. Even by consulting only standard Aristotelian textbooks, Mill says, one can see that logicians do not limit what they say about terms and propositions to what is necessary for understanding the reasoning process. Furthermore, he adds, a more just view of logic would see logic as most do, as a science or art comprising “all the instructions which philosophy could furnish towards the right employment of words, as an instrument for the investigation of the truth.” By adjoining the insights of Locke and others along these lines, Mill thinks logicians could bring logic “to a degree of perfection approaching to that which the theory of the reasoning process attained in their hands.” Whately’s discussion of the syllogism, like that of Aldrich, is “clear and accurate”, Mill says, but by adhering too closely to Aldrich in the first 2 parts, his treatment there is woefully inadequate. Mill backs up his evaluation with several specific criticisms of Whately’s discussion of predication and definition, and he offers some ideas of his own (which he had gleaned in part from earlier logics) in order to illustrate what might be done to improve these parts of logic.
Another aspect that Mill dislikes about Whately’s logic is his dismissal of a logic of induction. On the whole Mill agrees with Whately’s approach to induction and his defense of the syllogism against its inductivist detractors. But he does not think this is any reason to slight the logic of induction.
The philosophers who have spoken in such high terms of the desirableness of an inductive logic, meaning thereby rules for performing induction, have said no more than the truth; but the rules of correct deduction are not less essential, nor is it any objection to the Aristotelian logic that, professing only to give rules for one of these necessary operations, it affords no means of dispensing with the other. An inductive logic would be highly useful as a supplement to the syllogistic logic, not to supersede it.
An inductive logic might not be “logic” in the same sense as deductive logic, he says, but looking beyond the name to the phenomena it refers to, one can see its intrinsic value. Mill’s later view of the proper relationship of induction and deduction and of the crucial significance of induction is still in the future, but already at this time he holds the belief that an inductive logic can be constructed and that it will be a valuable addition to scientific methodology.
What is different about Mill’s position on inductive logic is that he holds it without in the least disparaging deductive reasoning or the syllogism. This is an attitude which he shared with Bentham and others of his generation, and which seems already to have been implanted in him by his early studies in Aristotelian logic (1818) supervised by his father, who did not accept the common view of logic’s inutility.
Knowing that Mill was early catechized on the importance of syllogistic reasoning over against its detractor’ criticisms also enables us adequately to understand the opening passage of the review in which Mill states his view of the historical significance of Whately’s logic. He there says, in essence, that a defense of syllogistic logic was bound to come sooner or later, given the sporty of the age.
There is a bit of literary flourish in Mill’s writing on Whately’s logic in the idea that Scottish common sense philosophy was as good as dead and that Whately merely did the inevitable, but given our understanding of the revival of Aristotelian logic which had been gathering momentum prior to Whately’s publication and with which Mill seems to have been familiar, at a least in part, it is clear that his description is only an exaggeration, not a fabrication. Moreover, his final remark that it is Whately’s work which marks a new appreciation for and sound defense of syllogistic logic balances off his negative assessment and must be given due weight.
William Hamilton was doubly educated, first in Scotland and then at Oxford. In 1803–1804 session he studied logic under Jardine and seems to have been a fairly good, though irregular, student. Hamilton had a great deal of respect for Jardine as a teacher, but exactly what he learned from him is not clear. He certainly did not follow Jardine in his view that logic culminated in the inductive logic of Bacon, nor did he accept Jardine’s admixture of logic and epistemology.
Memoir of Sir William Hamilton, Bart. Professor of Logic and Metaphysics in the University of Edinburgh — J Veitch 1869
After spending one year at Edinburgh studying medicine, Hamilton proceeded to Oxford as a Snell Exhibitioner. He matriculated, according to the conditions of the scholarship, at Balliol, where the master of the College, John Parsons, one of the foremost reformers of Oxford’s examination system, was busily attempting to convert the place into a respectable academic institution.
While Hamilton was an undergraduate at Oxford, Copleston’s work on Kett’s logic appeared and the debate between Copleston, Playfair, Davison, and Drummond took place. Hamilton followed the debates and distinctly sided with Copleston, Oxford, and traditional logic.
Hamilton largely prepared himself for his B.A. exams unaided, becoming known as “the most learned Aristotelian in Oxford.” This is the assessment of another Snell Exhibitioner of the time, James Traill. It is repeated by L Stephen in his 1890 article on Hamilton in the Dictionary of National Biography.
Sir William Hamilton in Dictionary of National Biography — Leslie Stephen 1890
Hamilton never published a systematic treatise on his system of logic, but through his class lectures and his students he spawned a whole school of logic and metaphysics. These lectures, originally written up around 1837, were posthumously published by his followers Henry Longueville Mansel and John Veitch in a two volume work entitled Lectures on Metaphysics and Logic.
An exposition of his logical doctrines was also published during his lifetime by another of his disciples, Thomas Spencer Baynes, as An Essay on the New Analytic of Logical Forms (1850).
And even earlier than this (in or before 1837) Hamilton appended a concise, two page summary of his outlook on logic to the article on “Logic” in the 7th edition of Encyclopaedia Britannica.
The work which initially and immediately established Hamilton’s reputation as a logic scholar, however, was his April, 1833 review “Recent Publications on Logical Science” in the Edinburgh Review. In this article Hamilton takes under review 10 different publications in logic that had appeared since 1826, including Whately’s Elements of Logic (3rd edition, 1829), Bentham’s 1827 Outline of a New System of Logic, Hill’s fourth edition of Aldrich’s Artis Logicae Rudimenta (1828), Samuel Hinds’ abridgment of Whately’s logic (1827), John Huyshe’s 1833 edition of Aldrich’s logic, and George Moberly’s Introduction to Logic.
Hamilton certainly does not deal with them all separately or in great depth. The main focus of the review is Whately’s work and others’ comments upon or extensions of it.
Hamilton considers all the works to be “correlative” to Whately’s and so excuses himself from considering the other works on their own. This is not completely true, for Hill’s Aldrich was first published before Whately’s work came out, Huyshe’s logic is primarily a commentary on Aldrich, and Bentham’s logic contains a number of ideas quite unrelated to Whately’s — such as the quantification of the predicate, for instance.
Hamilton opens his article with a historical discussion of the condition of logic education in the British universities before the appearance of Whately’s publication. He claims that just when “logic seemed in Oxford on the eve of following metaphysic and psychology to an academic grave, a new life was suddenly communicated to the expiring study, and hope at least allowed for its ultimate convalescence under a reformed system.” As Hamilton gauges it, “This was mainly effected by the publication of the Elements of Dr. Whately”.
Having established that there is a stirring in logic at Oxford and that Whately should be given the major credit for it, Hamilton turns to ask, “what value are we to rate these new logical publications”? Though he grants that “None of the works are the productions of inferior ability”, that “they are respectably executed”, and that Whately’s work in particular “is the effort of an intellect of great natural power”, yet the treatises are all rather disappointing, he says, for “They are rarely, indeed, wise above Aldrich”.
This is meant as strong reproach, for Hamilton has almost nothing good to say about Aldrich’s compendium of logic: “as a full course of instruction, … it is utterly contemptible.” Whately’s logic, while the best of the lot, is still weighted down by its tie to Aldrich.
His work, indeed, never transcends, and generally does not rise to, the actual level of the science; nor, with all its ability, can it justly pretend to more than a relative and local importance. Its most original and valuable portion is but the insufficient correction of mistakes touching the nature of logic, long exploded, if ever harbored, among the countrymen of Leibnitz, and only lingering among the disciples of Locke.
Hamilton here alludes to the two main issues which are the foci of his discussion throughout the remainder of the article: the definition and subject matter of logic and Whately’s defense of syllogistic logic. The first matter is in fact Hamilton’s main concern. He analyzes at length Whately’s view of logic as science and art and his view of logic’s connection with reasoning and with language. As he does so, he draws upon a wealth of historical information, now and again convicting whately and his associates of gross ignorance of logical trends, both inside and outside the British Isles.
On the matter of Whately’s defense of logic against its critics, Hamilton acknowledges this to be the work’s strength, yet he does not spend much time discussing it. Either Hamilton was so pre-occupied with his own concern — a proper view of the nature of logic — or he felt that this issue was no longer in need of close examination; or both.
He gives a brief defense of the way in which the scholastics viewed the syllogism with respect to science, saying they ever thought of logic as a vehicle for pursing physical knowledge about the world, and he devotes the last third of his article to an exposition of the nature of induction from a strictly logical (that is, Hamiltonian) point of view, but he completely ignores Whately’s longer and more important discussion of the value of syllogistic reasoning for acquiring new knowledge. No reason for this is given in the article.
The omission is glaring from our perspective.
It also seems typical, for Hamilton does not expend much energy in defending logic; he instead assumes its value and attempts to do logic, something Whately’s logic made it possible for people to engage in again in Great Britain — through the very defense that Hamilton slights.
Everyone who has investigated the development of logic in Great Britain during the first half of the 19th century is unanimous in holding that Whately’s logic is an important part of the revival that occurred there. There is less agreement, however, on precisely what its role was within this revival. Before delineating our own viewpoint on this matter, it will be helpful to state and compare some conclusions made by previous historians of logic. This will give us a number of actual positions to interact with and build upon, and it will enable us to set down our own ideas in clearer contrast to what has already been said by others.
Kubitz, in his pioneering work half a century ago on the intellectual development of Mill’s logic, gave what is probably the ordinary viewpoint of Whately’s place in the revival of British logic, only stated in rather extreme form. Leaning heavily on William Hamilton’s assessment of the state of logic in England, Scotland, and Ireland before Whately arrived on the scene, he finds Whately’s work to be the salvation of logic in Britain.
Mill’s comment in 1828 about the revival of syllogistic logic being inevitable might at least have given Kubitz pause to consider this idea and investigate the matter further, but Mill’s logic, not his view of Whately, was Kubitz’s main concern.
A similar viewpoint is expressed by Brody, both in his doctoral dissertation of 1967 and in his 1976 article on Whately in the Dictionary of Scientific Biography. Brody claims that Whately’s logic “was the first book on formal logic to be written in Great Britain since Aldrich’s Artis Logicae Rudimenta”, and that “In a short time, Whately’s book revitalized the study of formal logic in England.”
In his view, Whately’s logic amounted to a revolt in logic against Locke and the 18th century philosophers. He, too, draws on William Hamilton’s remarks about logical study being about ready to expire in Great Britain when Whately published his Elements of Logic.
In 1976 Brody specifies this importance by stating (without argument) that “Whately’s work laid the philosophical foundations for the revolutionary developments in logic (notably Boole’s algebra of logic) that took place in England during the 19th century.” However, his examination of Whately’s ideas on all these points is rather slight, and his treatment of the critics of logic whose arguments Whately counteracts is very scant, even inaccurate in spots.
Mary Prior, in her short 1967 article on Whately in the Encyclopedia of Philosophy, notes that Whately is considered by De Morgan to be the restorer of logical study in England, but she queries how far this assessment can be taken without qualification. For if it were so, one would “expect to find adumbrations of [later] work [such as that of Mill, De Morgan, and Boole] in Whately, but in his systematic and formal treatment of logic there are remarkably few.” She therefore locates the value of the work in its being a “moral metalogic”, meaning approximately what Mill did in his review, that Whately talks better about what logicians should be doing than actually does it. He can be considered the restorer of logic because he redefined the subject matter of logic and gave the first “convincing reply to the charges leveled against logic from the time of the Renaissance.”
Howell stresses the identity of Whately’s approach with that of Aldrich and intimates that a revival of traditional logic (Aldrich) was nearly in full swing by the time Whately published his work. Because he strongly identifies with the “new logic” of the 17th and 18th century (the inductive and epistemological versions developed by Locke, Reid, Stewart, and others), Howell is totally out of sympathy with Whately’s approach, and this partiality shows in his treatment. McKerrow defends Whately against Howell’s interpretation and holds that Whately is the reviver, though he also had an important predecessor and associate in Copleston. Yet McKerrow’s interest in Whately is not with his role as a restorer of logic, so this topic does not receive much of his attention.
As this brief recital indicates in several places, the recent assessments of Whately’s logic draw heavily on earlier evaluations in the secondary literature. The works that are used are:
Hamilton’s 1833 article Mill’s 1828 article and also his book of 1843 Robert Blakey’s 1851 work on history of logic De Morgan’s article on English logic (1860) Samuel Neil’s two-part article on Whately of 1862 Alexander Campbell Fraser’s 1864 address on Whately
Robert Blakey was quite unsympathetic to Whately’s traditional approach to logic, but he agreed with Mill regarding the importance and nature of Whately’s accomplishment.
Augustus De Morgan notes that a real revival in logic had taken place in England (by which he means all 3 countries) during his life-time and in which he had been one of the major participants. Whately’s logic he assigns to the pre-history of this revival, saying, however, that Whately was the person responsible for making logic a respectable field of investigation.
De Morgan states that Whately’s text enable logic to gain a new hearing for itself in a setting that was altogether as bad as Hamilton had said it was. De Morgan specifies several things about the book that made it so effective in reasserting the importance of logic, but he fails to make any remarks about the substance or nature of Whately’s defense of logic. He also does not treat the issue of whether and to what extent Whately alone should be credited with the occurrence. He merely says that it was due to his Elements of Logic.
Because of his perspective of Whately’s role in the revival, De Morgan takes it somewhat ill of William Hamilton, his perennial opponent, for being so critical of Whately. De Morgan bowed to Hamilton’s historical erudition and conceded that the review was a milestone in the development of British logic, but he thought Hamilton’s critique of Whately was out of place.
The true “place and office of the work”, according to De Morgan, is that of stimulating further interest in logic through silencing the criticism of the syllogism, not in advancing the field itself.
Samuel Neil wrote a two-part article on Whately in the 1862 volume of his magazine The British Controversialist. Like Hamilton, Neil prefaces his comments on Whately’s logic by discussing the climate of logic in England at that time and earlier in order to give the reader a sense of what Whately was up against. He also notes that Whately was not the sole reformer, but that he was partly indebted to Copleston’s ideas on logic for his own work. This theme is elaborated and modified in a later article of the series, where much more credit is given to Copleston and the Oxford examination reforms for reviving the study of logic.
In examining the work itself, Neil repeats both Bentham’s and Hamilton’s criticisms, but he notes that these are relatively minor. Like De Morgan he thinks that Hamilton’s critique of Whately’s logic is too harsh, particularly regretting Hamilton’s accusation that the Elements of Logic never rose to the level of science and had only a relatively and minor significance. Neil finds several aspects of Whately’s logic commendable. He praises the introductory portions of the work, saying they show “great vigor and acuteness of intellect” and claiming that “The combined charm of the style, and instructiveness of the matter, justly entitle [the Elements of Logic] to its popular pre-eminence among modern logical manuals.”
Neil’s most substantial reservations about Whately’s work concern the final chapter on the province of reasoning. Some of this essay, Neil observes, repeats or elaborates what had already been said in the introductory section and should have been combined with it. Moreover, the parts on induction and discovering new knowledge by means of deductive reasoning, Neil says doesn’t convince the readers.
Neil’s position on the role of Whately’s work is somewhat similar to De Morgan’s, then, only it goes into more specific detail on the merits of the work. Due to Whately’s publication, logic once again became a respectable field of study at Oxford and many were encouraged to think and write about logic, even if not from a common approach with that of Whately himself.
Fraser circumscribes Whately’s position in the movement as the restorer of logic, as the one who brought logic back above the threshold of esteem necessary to attract bright thinkers to seriously study it. Whately’s logic, he notes, is still very traditional, but in fleshing it out and breathing new life into it by means of a clear and animated style, his work made the subject come alive for students at Oxford and elsewhere.
Whately cannot be said to be part of the later revival of logic, according to Fraser. His part was that of a forerunner who gave the next generation in logic a place from which to initiate their reforms and the elements for understanding what it was that was being reformed. In Fraser’s own words,
In the hands of some [Hamilton, for example], the forms of syllogistic logic are undergoing a revolution; by others [such as Mill], logical methods for ascertaining premises, induction and otherwise, are presented in a new light. But of this scientific movement in advance within the field of logic, we find no trace in the unpretending manual of Whately, in which there is no sight of extensive and accurate acquaintance with, or indeed care for the literature of the speculative foundations of the science he undertook to recommend to an unbelieving generation. This was not the sort of service he was ready to render.
[T]here is no mark of his hand in the revolution which in this generation has been going on in the very scientific framework itself on which he was accustomed to show up fallacies. Yet by the qualities of his mind and character … he, as it were, secured the public ear for logic, leaving it to others to address to that ear logical discussions and speculations from which he instinctively turned aside. The student of logical science as evolved in the compendium of Whately, thus finds himself in a new world when he sees around him the logical speculations, or the discoveries, of Hamilton and Mansel and De Morgan, or of Mill or Whewell.
In evaluating Whately’s contribution to the history of British logic, then, Fraser concludes that Whately’s work was seminal in again focusing attention on logic as a legitimate field of investigation, but that it did not presage or even try to keep abreast of the later revival that occurred. In all this Fraser’s attention is directed primarily to the relation of Whately’s work to what came after it. He credits Whately’s work with being the one which rejuvenated logical study in Great Britain, but he does not really explain why there was a need for this — except to castigate those who “perverted [logic] into a dry art of wrangling, and a minister of verbal controversy, [so that] it deservedly fell into decay among us in this country.” He also does not tell what Whately did to restore logic beyond writing a college text in a more interesting style than his predecessors had. And finally, he does not give any analysis of how Whately stood among his contemporaries in his attitude toward logic.
A comparison of the various assessments of Whately’s logic by writers of this century and last reveals, if nothing else, that a synthesis of the various aspects of the issue still requires to be made.
The earlier writers are on the whole clearer and more correct on how Whately’s logic ties into the developments which they have witnessed that followed its publication, but they do not uniformly agree on what the merits of the work are nor why it was needed. When they deal with the negative trends which Whately is combating, their narrative is often over-simplified and diffuse. Moreover, all of the historians without exception fail to show how Whately’s logic sits within its own milieu.
They generally tend to be ignorant of the positive indicators that signal a revival of Aristotelian logic gathering strength in the British Isles before Whately wrote his treatise; or, like Neil, who seems eventually to realize that something was happening before Whately wrote his work, they do not go into the matter with any depth and are too vague to be accurate. Howell, too, sees that Whately’s work had its precursors but he focuses on the role of Aldrich, which is really the wrong place to look. As a consequence of this lack of knowledge of antecedent works, previous historians have also been unable to determine precisely where Whately advances beyond his predecessors and where he is merely synthesizing their earlier arguments and outlooks. Chapter 1 and 2 above provide us with the materials to correct this state of affairs. To conclude this study, then, we will give a summary of the place and nature of Whately’s Logic as we see it, drawing upon our analysis of the work from the present chapter plus our analysis and findings of the earlier chapters.
It should be evident from our discussion in the second chapter that Whately’s defense of Aristotelian logic was not an isolated phenomenon. A revival of sorts was under way in Scotland, Ireland, and England before Whately became a fellow at Oxford (1811).
According to Jongsma there are many early nineteenth century events in British logic that support the thesis that a return to traditional logic was already in the offing before Whately arrived on the scene to defend logic in mid-1823 and 1826. These things may not all have greatly affected university education in logic, and there was still a definite need for a strong defense of logic to be made in the context of a treatise on logic proper, but with hindsight we can see that the situation was not quite as bleak as Hamilton and those who follow him make it out to be. Here Mill seems to be closer to the truth. Mill’s thinking of the comeback of traditional logic as inevitable is obviously exaggerated, but probably less so than the opposing viewpoint.
Knowing that Whately was not the sole defender of syllogistic logic and that there were several strong stands made before he published his work, we now have the more difficult task of determining just what his role was within the “restoration” of traditional logic.
Whately’s work derived from Gillies’ defense of logic in his “New Analysis of Aristotle’s Works” via Copleston. Copleston’s remarks on Aristotle’s view of induction and his idea that logic is an art of rightly using language was at least bolstered by Gillies’ outlook even if it did not derive from it.
Whately’s possible debts to Kirwan are in the first place for his popularizing the notion that logic is both a science and an art. Also, Kirwan, like Whately, holds that all reasoning is potentially syllogistic, that the syllogistic form only fills out and makes regular ordinary reasoning. Whately, however, spells out the relation between reasoning in general and the syllogism more explicitly than Kirwan. He also makes this thesis a central tenet of his defense of logic and syllogistic reasoning, while Kirwan does not.
It is also possible that Lyall was familiar with Kirwan’s work on logic, for he too has some of these same stresses on reasoning. However, he views logic as science alone; he does not recognize the value of logic as an art of reasoning. This distinguishes his position from Whately and puts Whately closer to Kirwan. However, some of Lyall’s remarks regarding Stewart’s criticisms of “demonstrating demonstration” and the inutility of syllogistic reasoning adumbrate those of Whately. Whately does not make all of Lyall’s distinctions and his remarks are far more cogent than Lyall’s, but the similarity between parts of Whately’s arguments and Lyall’s, even down to using the same or very similar illustrations, leads one to suspect that Whately knew and made use of Lyall’s article.
Memoirs of Richard Whately, Archbishop of Dublin. With a glance at his contemporaries and times — W J Fitzpatrick 1864 Whately’s Theory of Rhetoric — R E McKerrow 1982
Whately adds a note that he draws from Analytical Dialogues he had compiled from conversations with Copleston in the preface to 1844 edition of his Logic.
The point which Copleston stressed above all else in his writings was that induction was not to be pitted against the syllogism. This stress is also strong in Whately. Whately, like Copleston, acquits Bacon of any fault on this score, saying that Aristotle’s and Bacon’s induction are the same in theory, though the ancients jumped to conclusions too quickly in physical science. Copleston also noted that an inductive argument could be formulated syllogistically, though Aldrich had misconstrued how this was done. Whately follows Copleston here, too. Copleston does not stress the fact that induction is primarily a method of investigation and so lies outside of logic — even Whately gets stronger on this as he goes — but the related idea that investigation and reasoning must be distinguished and the syllogism not accused of failing to do something it was not intended to do is present in his writings. In further discussions with Whately later on, Copleston may have made this clearer, or Whately himself may have drawn out his distinction between induction as investigation and induction as reasoning from what Copleston had already said. So while this view is not as strong in Copleston as it is in Whately, it definitely arises out of Copleston’s writing.
Whately’s section on syllogistic reasoning and discovery of new knowledge does not have any precedent in Copleston’s writings, except in Whately’s denial that the syllogism is an organon of science in an absolute sense.
Copleston not only influenced Whately’s defense of logic; he also molded Whately’s positive outlook on logic. The emphasis on logic as science is not in Copleston’s writings, but the emphasis on logic as art is. Whately’s stress on the place of language in logic is also probably due to Copleston. Copleston shies away from viewing logic as an art of reasoning, but Whately’s distinction between reasoning and reason, between drawing conclusion and various other intellectual operations, and Whately’s circumscribing logic as having to do just with reasoning would have met Copleston’s concern.
Copleston’s view of the syllogism as the form into which all reasoning can be put, as the logical framework underlying all argumentation, is developed by Whately into the notion that all reasoning is potentially syllogistic and that the syllogism is only a peculiar form of reasoning, not a particular kind of reasoning.
Like Copleston, too, Whately sees the function of logic (as an art) primarily as an arbiter of argumentation. By means of analyzing arguments into syllogistic form, one can clearly detect and reject fallacious arguments. Logic does not direct one into a knowledge of the truth, but it helps one recognize valid arguments and terminate disputes.
In all these ways Copleston contributed to the formation of Whately’s outlook on logic. In addition Whately sometimes borrows Copleston’s own words or examples to state or illustrate his point; we have noted this several times above. The accumulated evidence, then, points to the fact that perhaps Whately was not exaggerating too much after all when he credited Copleston essentially with joint authorship. Should Copleston instead, then, be considered the reviver of traditional logic in England, as Neil seems to assert?
Who should be given the credit is to some extent immaterial, of course, but to go from giving Whately all the credit to giving half of it to Copleston would be wrong. Whately obtained his outlook and basic ideas — his “principles” — primarily from Copleston, but he made them his own and developed them into a more or less coherent system of logic, something Copleston never did. It is a truism that ideas alone are insufficient to effect a reform; they need concrete embodiment in the right form at the right time and in the right place in order to exert intellectual leverage on the minds and actions of others and become historically potent.
Copleston’s ideas had their impact in their written and spoken forms among his readers and students, but they bore most fruit in and through Whately. It was not until Whately’s publication came out as a textbook in logic which could be used at Oxford and elsewhere that traditional logic was adequately defended against the charges of its critics.
Before Whately’s publication there were a number of somewhat isolated and impartial defenses of logic made. Whately solidified the defense and gave a rather complete reply to the various criticisms. His defense of deductive reasoning as being able to discover new knowledge results is particularly decisive, even if not concise or clear as it might have been. Here Whately’s work goes far beyond anything that had [been?] said before. It is this part of the work, in Jongsma’s view, that makes the Elements of Logic so outstanding; it makes his contemporaries once again know that they ought to stop devaluing deductive reasoning for scientific work.
Our considerations of the ideas of Copleston and various other predecessors, therefore, are meant to put Whately within the context of his age and to provide an antidote to the outlook which sees Whately’s defense as an isolated phenomenon. They are not meant so much to contradict as to balance off the received opinion of then and now that Whately is the sole restorer of logic and to assist us in defining just what there is about the work which deserves the acclaim. Whately is indeed the restorer of logic in Great Britain, though he did not stand alone.
George Cornewall Lewis was prompted to issue a 150 page pamphlet in 1829 entitled “An Examination of Some Passages in Dr. Whately’s Elements of Logic”. This work deals with the notions of predication and classification (something Mill had also discussed) and with non-categorical syllogizing. Its existence given the special nature of its subject matter, is an indication of the interest which Whately’s logic sparked.
An abridgment of Whately’s logic was published by Samuel Hinds (1793–1872) and an English translation with commentary of Aldrich’s logic by John Huyshe (1802 – 1880) which draws upon Whately for some of its commentary.
Fourth edition of Hill’s commentary of Aldrich also shows influence of Whately.
George Moberly’s 1830 Introduction to logic is another technical treatise out of Oxford in the style of the time with apparent influences of Whately.
More works could easily be added to this list to illustrate Whately’s influence on the revival of logic; just citing the repeated printings of Whately’s Elements of Logic would be enough to establish the works’ enduring popularity and its range of influence. No other logic of the time came near to equalling it. And that a revival of logic was inaugurated by Whately’s publication is indisputable — between 1826 and 1847, when both Boole and De Morgan published their logics, logic texts of all sorts came off the press at the the rate of better than one per year, and this does not include journal articles related to logic.
Yet another indication of the works’ significance is the fact that the most important logicians of the time were raised on Whately’s logic or first made their debut in reviewing it. This list of logicians from the next generation highlights the importance of Whately’s work but it also points out the need to delimit the role which the Elements of Logic played, for each of the logicians mentioned went in a different direction than Whately. Whately remained committed to the standard version of traditional logic, but the others did not. Hamilton, Thomson, and De Morgan each worked to extend the boundaries of syllogistic logic by introducing other forms of propositions. Boole used the techniques of algebra to calculate the consequences of premises appropriately symbolized as equations, so bringing mathematics and logic into closer union. And Mill returned to work out the ideal of an inductive logic espoused by Bacon, Reid, and Stewart, thus wedding philosophy of science to logic.
With such disparate results, how can Whately be considered responsible for reviving logic in Great Britain? The answer of De Morgan, Fraser, and others must be ours as well. Whately’s work gave new life to the study of logic but it did not dictate the future direction of logical investigations. Whately’s logic was directed at the past in order to defend syllogistic reasoning against the critics of Aristotelian logic. It restored confidence in the value of deductive reasoning and in the importance of the subject matter carved out by Whately for logic. But it failed to convince people that the positive goals of the critics — an inductive logic — was unattainable.
Outside influences, such as Kant’s philosophic of logic, made inroads in British logic through the teaching and writing of William Hamilton and his followers. And, though it was not recognized to be as important then as it is today, the cross-fertilization provided by the analytic trend in British mathematics which Boole brought to logic gave logic a powerful new impulse for development. All these things, while they may not have been completely unthinkable without Whately, nevertheless follow Whately’s work and greatly benefit from his defense of traditional logic. Whatever its time-bound character, then, Whately’s logic deserves to be known as the work which made possible the revival of logic in Great Britain.